Question 1

The percent p of high school students who participate in sports at a public high school can be modeled by 10 p $16 x = 224$, where $x$ is the number of years after 2010 . Interpret the slope as a rate of change if $x$ is the independent variable.

Accepted Answer

The slope in the equation $16x = 224$ is not directly given, but in the context of the problem, it seems there's a misunderstanding in the equation's presentation. Assuming the correct interpretation involves a rate of change, a slope of 16 in a linear equation typically indicates the rate of change. However, without the correct equation format (like y = mx + b), we deduce the intended meaning is an increase of 1.6 percent per year, considering common sense and typical scenarios of percentage change in such contexts.

Question 2

Find the rate of change. Use appropriate units.

Accepted Answer

The answer of

Find the rate of change. Use appropriate...

Question 3

The relationship between the number of units sold by a company and the profit is linear. If 5 units sold results in $110 profit and 37 units sold results in $814 profit, find the marginal profit.

Accepted Answer

The marginal profit is the change in profit divided by the change in units sold. The change in profit is $814 - $110 = $704, and the change in units sold is 37 - 5 = 32. Thus, the marginal profit is $704 / 32 = $22 per unit.

Question 4

The percent p of high school students who participate in sports at a public high school can be modeled by 10p - $24 x = 196$ ,where x is the number of years after 2010. Interpret the p intercept of the graph of this function.

Accepted Answer

The p-intercept occurs when x = 0, which represents the year 2010. Solving 10p = 196 gives p = 19.6, meaning 19.6% of students participated in sports in 2010.

Question 5

Determine whether or not the function is linear. If it is, determine the slope and interpret it.
-The population of a small town is given by P $\mathrm { P } ( \mathrm { t } ) = 59 \mathrm { t } + 12,350$ , where t is the number of years past 2010.

Accepted Answer

The function $P(t) = 59t + 12,350$ is linear because it can be written in the form $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept. The slope is 59, which means the population increases by 59 people each year since 2010.

Question 6

The cost of manufacturing a molded part is related to the quantity produced during a production run. When 100 parts are produced, the cost is $300. When 400 parts are produced, the cost is $2700. What is the marginal cost of
The function?

Accepted Answer

The marginal cost is calculated by the change in cost divided by the change in quantity. From 100 to 400 parts, the cost increases from $300 to $2700, a change of $2400. The change in quantity is 300 parts (400-100). Thus, the marginal cost is $2400 / 300 = $8.00 per part.

Question 7

Determine whether or not the function is linear. If it is, determine the slope and interpret it.
-The height of an object $t$ seconds after being dropped from an altitude of 249 feet is given by the function h(t) = $- 16 t ^ { 2 } + 249$

Accepted Answer

The function $h(t) = -16t^2 + 249$ is not linear because it includes a term with $t$ raised to the power of 2, indicating it is a quadratic function.

Question 8

In a certain town the annual consumption, b, of beef (in pounds per person) can be estimated by $b = 34 - 0.5 t$ where t is the number of years since 2010. Find and interpret the t-intercept of the graph of this function.

Accepted Answer

The answer of In a certain town the annual consumption,...

Question 9

The cost of tuition at a community college is given $$C ( x ) = 490 + 54 x$$ x, where x is the number of credit hours. Interpret the slope of this function as a rate of change.

Accepted Answer

The slope of the function, which is 54, represents the rate of change of the cost of tuition with respect to the number of credit hours. This means the tuition increases by $54 for each additional credit hour.

Question 10

Determine whether or not the function is linear. If it is, determine the slope and interpret it.
-The value of a particular car is given by V(t) $V ( t ) = 22,000 - 3200 t$ t, where t is the age of the car in years.

Accepted Answer

The function $V(t) = 22,000 - 3200t$ is linear because it can be written in the form $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept. The slope is -3200, which means the car depreciates by $3200 each year.

Question 11

The population of a small town can be modeled by P $$P = - 33 t + 12,800$$ , where t is the number of years since 2010. Interpret the slope of the graph of this function as a rate of change.

Accepted Answer

The slope of the graph, which is -33, represents the rate of change of the population with respect to time. Since it is negative, it indicates the population is decreasing by 33 people per year.

Question 12

The cost of a rental car for the weekend is given by the function C(x) $$C ( x ) = 146 + 0.25 x$$ , where x is the number of miles driven. Find the slope of the graph of this function and interpret it as a rate of change.

Accepted Answer

The slope of the graph, which is the coefficient of $x$ in the function $C(x) = 146 + 0.25x$, is 0.25. This represents the rate of change, indicating that the cost of the rental car increases by $0.25 for each additional mile driven.

Question 13

Determine whether or not the function is linear. If it is, determine the slope and interpret it.
-The cost of tuition at a community college is given $C ( x ) = 485 + 68 x$ x, where x is the number of credit hours. Find and interpret the C-intercept of the graph of this function.

Accepted Answer

The function is linear because it is in the form $C(x) = mx + b$. The slope is 68, meaning the tuition increases by $68 for each additional credit hour. The C-intercept is 485, which represents the base tuition fee without any credit hours.

Question 14

Determine whether or not the function is linear. If it is, determine the slope and interpret it.
-The cost of a rental car for the weekend is given by the function C(x) $C ( x ) = 137 + 0.25 x$ , where x is the number of miles driven. Find and interpret the C-intercept of the graph of this function.

Accepted Answer

The C-intercept is the value of the function when x = 0. In this case, C(0) = 137, so the C-intercept is 137. This means that there is a flat rate of $137 to rent a car in addition to the charge for each mile driven.

Question 15

In a certain town the annual consumption, b, of beef (in pounds per person) can be estimated by $$b = 35 - 0.4 t$$ where t is the number of years since 2010. What is the slope of the graph of this function? Write a sentence interpreting this value.

Accepted Answer

The slope of the graph of this function is -0.4, which indicates that the average consumption of beef in this town is decreasing by 0.4 pounds per person per year.

Question 16

In a certain town the annual consumption, b, of beef (in pounds per person) can be estimated by $b = 36 - 0.5 t$ where t is the number of years since 2010. Find and interpret the b-intercept of the graph of this function.

Accepted Answer

The b-intercept occurs when $t = 0$, which corresponds to the year 2010. Substituting $t = 0$ into the equation $b = 36 - 0.5t$ gives $b = 36$, indicating that the annual consumption of beef was 36 pounds per person in 2010.

Question 17

Determine whether or not the function is linear. If it is, determine the slope and interpret it.
-The cost of tuition at a community college is given $C ( x ) = 467 + 69 x$ x, where x is the number of credit hours.

Accepted Answer

The function $C(x) = 467 + 69x$ is linear because it can be written in the form $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept. The slope is 69, indicating that for each additional credit hour, the cost of tuition increases by $69.

Question 18

Suppose the monthly cost for manufacturing bar stools i $C ( x ) = 529 + 23 x$ x, where x is the number of bar stools produced each month. Find and interpret the marginal cost for the product.

Accepted Answer

The marginal cost is the derivative of the total cost function with respect to x, which in this case is $23. This means for each additional bar stool produced, the cost increases by $23.

Question 19

The population of a small town can be modeled by P $P = - 32 t + 13,500$ where t is the number of years since 2010. Interpret the P-intercept of the graph of this function.

Accepted Answer

The P-intercept occurs when t = 0, which corresponds to the year 2010. At t = 0, P = 13,500, indicating the population of the town was 13,500 in 2010.

Question 20

Suppose the monthly total revenue for manufacturing baseball bats is R(x) = 26.00x, where x is the number of bats sold each month. Find and interpret the marginal revenue for the product.

Accepted Answer

The marginal revenue is the derivative of the total revenue function with respect to x, which in this case is constant at $26.00. This means for each additional bat sold, the revenue increases by $26.00.

Quiz 1: Functions, Graphs, and Models; Linear Functions

The percent p of high school students who participate in sports at a public high school can be modeled by 10 p $16 x = 224$ , where $x$ is the number of years after 2010 . Interpret the slope as a rate of change if $x$ is the independent variable.

$Find the rate of change. Use appropriate units. A) \$ 4000 per year B) \$ 3000 per year C) - \$ 4000 per year D) - \$ 3000 per year$ Find the rate of change. Use appropriate units.

The relationship between the number of units sold by a company and the profit is linear. If 5 units sold results in $110 profit and 37 units sold results in $814 profit, find the marginal profit.

The percent p of high school students who participate in sports at a public high school can be modeled by 10p - $24 x = 196$ ,where x is the number of years after 2010. Interpret the p intercept of the graph of this function.

Determine whether or not the function is linear. If it is, determine the slope and interpret it. -The population of a small town is given by P $\mathrm { P } ( \mathrm { t } ) = 59 \mathrm { t } + 12,350$ , where t is the number of years past 2010.

The cost of manufacturing a molded part is related to the quantity produced during a production run. When 100 parts are produced, the cost is $300. When 400 parts are produced, the cost is $2700. What is the marginal cost of The function?

Determine whether or not the function is linear. If it is, determine the slope and interpret it. -The height of an object $t$ seconds after being dropped from an altitude of 249 feet is given by the function h(t) = $- 16 t ^ { 2 } + 249$

In a certain town the annual consumption, b, of beef (in pounds per person) can be estimated by $b = 34 - 0.5 t$ where t is the number of years since 2010. Find and interpret the t-intercept of the graph of this function.

The cost of tuition at a community college is given $C ( x ) = 490 + 54 x$ x, where x is the number of credit hours. Interpret the slope of this function as a rate of change.

Determine whether or not the function is linear. If it is, determine the slope and interpret it. -The value of a particular car is given by V(t) $V ( t ) = 22,000 - 3200 t$ t, where t is the age of the car in years.

The population of a small town can be modeled by P $P = - 33 t + 12,800$ , where t is the number of years since 2010. Interpret the slope of the graph of this function as a rate of change.

The cost of a rental car for the weekend is given by the function C(x) $C ( x ) = 146 + 0.25 x$ , where x is the number of miles driven. Find the slope of the graph of this function and interpret it as a rate of change.

Determine whether or not the function is linear. If it is, determine the slope and interpret it. -The cost of tuition at a community college is given $C ( x ) = 485 + 68 x$ x, where x is the number of credit hours. Find and interpret the C-intercept of the graph of this function.

Determine whether or not the function is linear. If it is, determine the slope and interpret it. -The cost of a rental car for the weekend is given by the function C(x) $C ( x ) = 137 + 0.25 x$ , where x is the number of miles driven. Find and interpret the C-intercept of the graph of this function.

In a certain town the annual consumption, b, of beef (in pounds per person) can be estimated by $b = 35 - 0.4 t$ where t is the number of years since 2010. What is the slope of the graph of this function? Write a sentence interpreting this value.

In a certain town the annual consumption, b, of beef (in pounds per person) can be estimated by $b = 36 - 0.5 t$ where t is the number of years since 2010. Find and interpret the b-intercept of the graph of this function.

Determine whether or not the function is linear. If it is, determine the slope and interpret it. -The cost of tuition at a community college is given $C ( x ) = 467 + 69 x$ x, where x is the number of credit hours.

Suppose the monthly cost for manufacturing bar stools i $C ( x ) = 529 + 23 x$ x, where x is the number of bar stools produced each month. Find and interpret the marginal cost for the product.

The population of a small town can be modeled by P $P = - 32 t + 13,500$ where t is the number of years since 2010. Interpret the P-intercept of the graph of this function.

Suppose the monthly total revenue for manufacturing baseball bats is R(x) = 26.00x, where x is the number of bats sold each month. Find and interpret the marginal revenue for the product.

Quiz 1: Functions, Graphs, and Models; Linear Functions

The percent p of high school students who participate in sports at a public high school can be modeled by 10 p 16x=22416 x = 22416x=224 , where xxx is the number of years after 2010 . Interpret the slope as a rate of change if xxx is the independent variable.

Find the rate of change. Use appropriate units.

The relationship between the number of units sold by a company and the profit is linear. If 5 units sold results in $110 profit and 37 units sold results in $814 profit, find the marginal profit.

The percent p of high school students who participate in sports at a public high school can be modeled by 10p - 24x=19624 x = 19624x=196 ,where x is the number of years after 2010. Interpret the p intercept of the graph of this function.

Determine whether or not the function is linear. If it is, determine the slope and interpret it. -The population of a small town is given by P P(t) =59t+12,350\mathrm { P } ( \mathrm { t } ) = 59 \mathrm { t } + 12,350P(t) =59t+12,350 , where t is the number of years past 2010.

The cost of manufacturing a molded part is related to the quantity produced during a production run. When 100 parts are produced, the cost is $300. When 400 parts are produced, the cost is $2700. What is the marginal cost of The function?

Determine whether or not the function is linear. If it is, determine the slope and interpret it. -The height of an object ttt seconds after being dropped from an altitude of 249 feet is given by the function h(t) = −16t2+249- 16 t ^ { 2 } + 249−16t2+249

In a certain town the annual consumption, b, of beef (in pounds per person) can be estimated by b=34−0.5tb = 34 - 0.5 tb=34−0.5t where t is the number of years since 2010. Find and interpret the t-intercept of the graph of this function.

The cost of tuition at a community college is given C(x) =490+54xC ( x ) = 490 + 54 xC(x) =490+54x x, where x is the number of credit hours. Interpret the slope of this function as a rate of change.

Determine whether or not the function is linear. If it is, determine the slope and interpret it. -The value of a particular car is given by V(t) V(t) =22,000−3200tV ( t ) = 22,000 - 3200 tV(t) =22,000−3200t t, where t is the age of the car in years.

The population of a small town can be modeled by P P=−33t+12,800P = - 33 t + 12,800P=−33t+12,800 , where t is the number of years since 2010. Interpret the slope of the graph of this function as a rate of change.

The cost of a rental car for the weekend is given by the function C(x) C(x) =146+0.25xC ( x ) = 146 + 0.25 xC(x) =146+0.25x , where x is the number of miles driven. Find the slope of the graph of this function and interpret it as a rate of change.

In a certain town the annual consumption, b, of beef (in pounds per person) can be estimated by b=35−0.4tb = 35 - 0.4 tb=35−0.4t where t is the number of years since 2010. What is the slope of the graph of this function? Write a sentence interpreting this value.

In a certain town the annual consumption, b, of beef (in pounds per person) can be estimated by b=36−0.5tb = 36 - 0.5 tb=36−0.5t where t is the number of years since 2010. Find and interpret the b-intercept of the graph of this function.

Determine whether or not the function is linear. If it is, determine the slope and interpret it. -The cost of tuition at a community college is given C(x) =467+69xC ( x ) = 467 + 69 xC(x) =467+69x x, where x is the number of credit hours.

Suppose the monthly cost for manufacturing bar stools i C(x) =529+23xC ( x ) = 529 + 23 xC(x) =529+23x x, where x is the number of bar stools produced each month. Find and interpret the marginal cost for the product.

The population of a small town can be modeled by P P=−32t+13,500P = - 32 t + 13,500P=−32t+13,500 where t is the number of years since 2010. Interpret the P-intercept of the graph of this function.

Suppose the monthly total revenue for manufacturing baseball bats is R(x) = 26.00x, where x is the number of bats sold each month. Find and interpret the marginal revenue for the product.

The percent p of high school students who participate in sports at a public high school can be modeled by 10 p $16 x = 224$ , where $x$ is the number of years after 2010 . Interpret the slope as a rate of change if $x$ is the independent variable.

$Find the rate of change. Use appropriate units. A) \$ 4000 per year B) \$ 3000 per year C) - \$ 4000 per year D) - \$ 3000 per year$ Find the rate of change. Use appropriate units.

The percent p of high school students who participate in sports at a public high school can be modeled by 10p - $24 x = 196$ ,where x is the number of years after 2010. Interpret the p intercept of the graph of this function.

Determine whether or not the function is linear. If it is, determine the slope and interpret it. -The population of a small town is given by P $\mathrm { P } ( \mathrm { t } ) = 59 \mathrm { t } + 12,350$ , where t is the number of years past 2010.

Determine whether or not the function is linear. If it is, determine the slope and interpret it. -The height of an object $t$ seconds after being dropped from an altitude of 249 feet is given by the function h(t) = $- 16 t ^ { 2 } + 249$

In a certain town the annual consumption, b, of beef (in pounds per person) can be estimated by $b = 34 - 0.5 t$ where t is the number of years since 2010. Find and interpret the t-intercept of the graph of this function.

The cost of tuition at a community college is given $C ( x ) = 490 + 54 x$ x, where x is the number of credit hours. Interpret the slope of this function as a rate of change.

Determine whether or not the function is linear. If it is, determine the slope and interpret it. -The value of a particular car is given by V(t) $V ( t ) = 22,000 - 3200 t$ t, where t is the age of the car in years.

The population of a small town can be modeled by P $P = - 33 t + 12,800$ , where t is the number of years since 2010. Interpret the slope of the graph of this function as a rate of change.

The cost of a rental car for the weekend is given by the function C(x) $C ( x ) = 146 + 0.25 x$ , where x is the number of miles driven. Find the slope of the graph of this function and interpret it as a rate of change.

In a certain town the annual consumption, b, of beef (in pounds per person) can be estimated by $b = 35 - 0.4 t$ where t is the number of years since 2010. What is the slope of the graph of this function? Write a sentence interpreting this value.

In a certain town the annual consumption, b, of beef (in pounds per person) can be estimated by $b = 36 - 0.5 t$ where t is the number of years since 2010. Find and interpret the b-intercept of the graph of this function.

Determine whether or not the function is linear. If it is, determine the slope and interpret it. -The cost of tuition at a community college is given $C ( x ) = 467 + 69 x$ x, where x is the number of credit hours.

Suppose the monthly cost for manufacturing bar stools i $C ( x ) = 529 + 23 x$ x, where x is the number of bar stools produced each month. Find and interpret the marginal cost for the product.

The population of a small town can be modeled by P $P = - 32 t + 13,500$ where t is the number of years since 2010. Interpret the P-intercept of the graph of this function.