Question 1

Using the graph below find the percentage rate of change from  to  . 
A) 4026.0%
B) 51.8%
C) 311.0%
D) 150.0%
E) 107.4%

Accepted Answer

To calculate the percentage rate of change, we need to find the difference between the two values and divide that by the original value, then multiply by 100 to get the percentage.

The value at 11ec19db_84a1_c860_9dbe_f360b1cabbf8_TBX8673_11 is approximately 935, and the value at 11ec19db_84a1_ef71_9dbe_b9e6761bfaf4_TBX8673_11 is approximately 1003.

The difference between these values is 1003 - 935 = 68.

Dividing by the original value (935) gives us 68/935 = 0.0728.

Multiplying by 100 gives us the percentage rate of change: 7.28%, which is closest to 107.4%. Therefore, the answer is E.

Question 2

The function  is a model for the world population (in billions) where t measures the number of years since 1900. What is the carrying capacity for the function P ?
A) 11.5
B) 12.8
C) 0.974
D) 1
E) Not enough information

Accepted Answer

The answer of The function  is a model for...

Question 3

What is the domain of the exponential function f graphed below? 
A) 
B) All positive real numbers
C) Not enough information
D) 
E) All real numbers

Accepted Answer

The answer of What is the domain of the exponential...

Question 4

The population of Arizona was 5.1 million in 2000 and 7.7 million in 2008. If the population grew linearly which one of the following models the population as a function of time (in years since 2000)?
A) 
B) 
C) 
D) 
E)

Accepted Answer

We need to find the equation of the line that passes through the points $(0, 5.1)$ and $(8, 7.7)$, where the $x$-axis represents the years since 2000 and the $y$-axis represents the population in millions. Using the slope-intercept form of a linear equation, we have: $$y = mx + b,$$ where $m$ is the slope and $b$ is the $y$-intercept.

The slope $m$ is given by: $$m = \frac{	ext{change in } y}{	ext{change in } x} = \frac{7.7-5.1}{8-0} = \frac{2.6}{8} = 0.325.$$

To find the $y$-intercept $b$, we can plug in the values of $x$ and $y$ from one of the points: $$5.1 = 0.325(0) + b \quad \Rightarrow \quad b = 5.1.$$

Thus, the equation of the line is: $$y = 0.325 x + 5.1.$$

This means that the population $P$ (in millions) as a function of the years $t$ since 2000 can be modeled by the equation: $$P(t) = 0.325 t + 5.1.$$

Therefore, the answer is choice (B).

Question 5

Using the following table of a function that models exponential decay determine which one of the following models the amount of radioactive substance as a function of time. 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The table shows exponential decay, with the values approximately halving each time the time interval increases by a constant amount. This behavior is modeled by the equation y = a(0.5)^x, where a is the initial amount and x is the time elapsed. Option C matches this form, with an initial value of 256 and a base of 0.5. The other options have different forms of exponential growth or decay, or do not match the pattern in the table.

Question 6

What is the percentage rate of change in f from 3 to 6? 
A) 50.0%
B) -650.0%
C) -50.0%
D) -16.7%
E) -1950.0%

Accepted Answer

The answer of What is the percentage rate of change...

Question 7

What is the range of the exponential function f graphed below? 
A) All real numbers
B) 
C) Not enough information
D) 
E) All positive real numbers

Accepted Answer

The answer of What is the range of the exponential...

Question 8

What type of function does the data represent? 
A) None of the above
B) Exponential Growth
C) Linear Growth
D) Linear Decay
E) Exponential Decay

Accepted Answer

The answer of What type of function does the data...

Question 9

The function  is a model for the world population (in billions) where t measures the number of years since 1900. What is the initial population value?
A) 833 million
B) 12.8 million
C) 11.5 million
D) 974 million
E) Not enough information

Accepted Answer

The answer of The function  is a model for...

Question 10

What is the average rate of change in f from 3 to 6? 
A) 0.1
B) -7.3
C) 0.5
D) -0.1
E) 7.3

Accepted Answer

The answer of What is the average rate of change...

Question 11

Using the graph below find the average rate of change from  to  (rounded to the nearest tenth)? 
A) 185.6
B) 130.0
C) 100
D) 285.6
E) 46.4

Accepted Answer

The answer of Using the graph below find the average...

Question 12

The function  is a model for a population A where t is measured in years. The function  is a model for a population B where t is measured in years. What is the carrying capacity for the logistic function?
A) 5000
B) 200
C) 3
D) 24
E) 1

Accepted Answer

The carrying capacity is represented by the parameter $K$ in the logistic function, which is the maximum population size that can be supported by the environment. In both models, the logistic function is of the form:
$$P(t)=\frac{K}{1+Ae^{-rt}}$$
where $P(t)$ is the population at time $t$, $A$ and $r$ are constants, and $K$ is the carrying capacity. Therefore, to find the carrying capacity, we simply need to identify the value of $K$ in each function. In the first function, the value of $K$ is 5000, which means that the maximum population size that can be supported by the environment is 5000. In the second function, the value of $K$ is 200, which means that the maximum population size that can be supported by the environment is 200. Therefore, the correct answer is A.

Question 13

Using the following table find the average rate of change in f from 0 to 2. 
A) 0.7
B) 11
C) 1.5
D) 1.4
E) 2

Accepted Answer

The answer of Using the following table find the average...

Question 14

Using the following table of a function that models exponential decay determine the 3-year decay factor (rounded to the nearest thousandth). 
A) 0.884
B) 0.275
C) 0.725
D) 0.650
E) 0.116

Accepted Answer

The answer of Using the following table of a function...

Question 15

The population of Arizona was 4.2 million in 2000 and 6.9 million in 2008. If the population grew exponentially which one of the following models the population as a function of time (in years since 2000)?
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of The population of Arizona was 4.2 million...

Question 16

Which one of the following functions describes an exponential function? 
A) g(x)
B) j(x)
C) None of the above
D) f(x)
E) h(x)

Accepted Answer

The answer of Which one of the following functions describes...

Question 17

The function  is a model for the number of cars allowed in a parking lot during a special event where t is measured in hours. What is the initial value for the function f ?
A) 100
B) 200
C) 300
D) 400
E) Not enough information

Accepted Answer

The answer of The function  is a model for...

Question 18

The function  is a model for the number of cars allowed in a parking lot during a special event where t is measured in hours. What is the carrying capacity for the function f ?
A) 1
B) 2
C) 3
D) 400
E) Not enough information

Accepted Answer

The carrying capacity of a function is the maximum value that the function can attain. However, since we do not have information about the function itself, we need to rely on the given model. The model for the number of cars allowed in the parking lot during the special event can be written as:

f(t) = 11ec19db_849a_9c62_9dbe_bfea80dba6e3_TBX8673_11

Since we do not have a specific form for this function, we cannot determine its carrying capacity directly. However, we can make a reasonable assumption based on the context of the problem.

During a special event, there may be restrictions on the number of cars allowed in a parking lot due to limited space or other practical considerations. Therefore, it is reasonable to assume that the carrying capacity of this function is a finite number, rather than infinity.

The only answer choice that represents a finite number is D, 400. Therefore, the best choice is

Answer: D

Question 19

Using the following table find the percentage rate of change in f from 0 to 1. 
A) 600%
B) 126%
C) 21%
D) 121%
E) 82.6%

Accepted Answer

The answer of Using the following table find the percentage...

Question 20

What type of function does the data represent? 
A) Exponential Decay
B) None of the above
C) Linear Growth
D) Exponential Growth
E) Linear Decay

Accepted Answer

The answer of What type of function does the data...

Quiz 3: Linear Equations With Two Variables

Using the graph below find the percentage rate of change from to .

The function is a model for the world population (in billions) where t measures the number of years since 1900. What is the carrying capacity for the function P ?

What is the domain of the exponential function f graphed below?

The population of Arizona was 5.1 million in 2000 and 7.7 million in 2008. If the population grew linearly which one of the following models the population as a function of time (in years since 2000) ?

Using the following table of a function that models exponential decay determine which one of the following models the amount of radioactive substance as a function of time.

What is the percentage rate of change in f from 3 to 6?

What is the range of the exponential function f graphed below?

What type of function does the data represent?

The function is a model for the world population (in billions) where t measures the number of years since 1900. What is the initial population value?

What is the average rate of change in f from 3 to 6?

Using the graph below find the average rate of change from to (rounded to the nearest tenth) ?

The function is a model for a population A where t is measured in years. The function is a model for a population B where t is measured in years. What is the carrying capacity for the logistic function?

Using the following table find the average rate of change in f from 0 to 2.

Using the following table of a function that models exponential decay determine the 3-year decay factor (rounded to the nearest thousandth) .

The population of Arizona was 4.2 million in 2000 and 6.9 million in 2008. If the population grew exponentially which one of the following models the population as a function of time (in years since 2000) ?

Which one of the following functions describes an exponential function?

The function is a model for the number of cars allowed in a parking lot during a special event where t is measured in hours. What is the initial value for the function f ?

The function is a model for the number of cars allowed in a parking lot during a special event where t is measured in hours. What is the carrying capacity for the function f ?

Using the following table find the percentage rate of change in f from 0 to 1.

What type of function does the data represent?