Question 1

Find or investigate the function as requested.
-Find a function f(n)whose domain is the set of natural numbers and the output produces the terms of the sequence 4, 16, 64, 256, . . . 
A) $4 n$
B) $4 ^ { \mathrm { n } }$
C) $\mathrm { n } ^ { 4 }$
D) There is no such function.

Accepted Answer

The sequence is a geometric sequence where each term is 4 times the previous term, starting with 4. The function that generates this sequence is $f(n) = 4^n$, where n is a natural number.

Question 2

Solve the problem.
-John is paid a weekly salary of $380 plus 4% of his sales. Draw a graph in which sales are measured on the horizontal axis and wages on the vertical axis. Then use the graph to estimate John's sales if his week's pay is $530.  
A)About $3757 
B)About $3745 
C)About $3750 
D)About $3760

Accepted Answer

The answer of Solve the problem.
-John is paid a weekly...

Question 3

Find or investigate the function as requested.
-If  t(n)  represents the nth term of a sequence for $\mathrm { n } \in \mathrm { N }$ and $t ( n ) = n ^ { 2 } + 2 n + 5$ , then is 29 a value of the function whose domain is  N ?
A) No
B) Yes

Accepted Answer

To determine if 29 is a value of the function $t(n) = n^2 + 2n + 5$, we substitute 29 for $t(n)$ and solve for $n$: $29 = n^2 + 2n + 5$. Simplifying, we get $n^2 + 2n - 24 = 0$, which factors to $(n+6)(n-4) = 0$. Thus, $n = -6$ or $n = 4$. Since $n$ must be a natural number ($n \in N$), $n = 4$ is the valid solution. Therefore, 29 is indeed a value of the function for $n \in N$.

Question 4

Solve the problem.
-The town of Appleville recorded the following dates and populations.  Draw a graph of the population as a function of time. What was the approximate population of Appleville in 2002?
A)11,000
B)12,000
C)13,000
D)10,000

Accepted Answer

The answer of Solve the problem.
-The town of Appleville recorded...

Question 5

Solve the problem.
-You brake your car from a speed of 60 mph. The table shows data that represent your car's speed versus the amount of time elapsed from the moment that you began to brake.  Graph the data. For what interval of time is the speed increasing? For what interval of time is the speed Decreasing? For what interval of time is the speed constant? 
A)

Elapsed Time (seconds)
0 to 4 seconds; None; 4 to 6 seconds

B)

Elapsed Time (seconds)
0 to 5 seconds; None; 5 to 6 seconds

C)

Elapsed Time (seconds)
None; 0 to 5 seconds; 5 to 6 seconds

D)

Elapsed Time (seconds)
None; 0 to 4 seconds; 4 to 6 seconds

Accepted Answer

The answer of Solve the problem.
-You brake your car from...

Question 6

Find or investigate the function as requested.
-Find a function f(n)whose domain is the set of natural numbers and the output produces the terms of the sequence 8, 11, 14, 17, . . .
A)n - 5
B)3n
C)3n - 5
D)3n + 5

Accepted Answer

The given sequence is an arithmetic sequence starting at 8 and increasing by 3 each time. The nth term of an arithmetic sequence is given by $a_n = a_1 + (n - 1)d$, where $a_1$ is the first term and $d$ is the common difference. Here, $a_1 = 8$ and $d = 3$, so $a_n = 8 + (n - 1)3 = 8 + 3n - 3 = 3n + 5$. Therefore, the function that generates this sequence is $f(n) = 3n + 5$.

Question 7

Find or investigate the function as requested.
-Find a function f(n)whose domain is the set of natural numbers and the output produces the terms of the sequence 1, 6, 11, 16, . . .
A)5n - 4
B)4n
C)5n
D)5n + 4

Accepted Answer

The sequence starts at 1 and increases by 5 each time. The formula 5n - 4 generates this sequence when n starts at 1 (for the first term), 2 (for the second term), and so on.

Question 8

Solve the problem.
-For its regular delivery service, a parcel service charges $22.50 for the first 5 pounds plus $1.50 for each additional pound. Draw a linear graph that can be used to estimate the cost of parcels Weighing 5 to 20 pounds. Use the horizontal axis for the weight and the vertical axis for the cost.Use the graph to estimate the weight of a parcel which costs $51.00. 
A) About $19 \mathrm { lb }$
B) About $24 \mathrm { lb }$
C) About $14 \mathrm { lb }$
D) About $27 \mathrm { lb }$

Accepted Answer

The answer of Solve the problem.
-For its regular delivery service,...

Question 9

Solve the problem.
-Crafty Bill's Cool Car Sales opened as a used car sales lot in 2006. The graph shows the number of cars sold as a function of time. What is the approximate number of cars sold in 2010? 
A)900
B)950
C)600
D)150

Accepted Answer

The answer of Solve the problem.
-Crafty Bill's Cool Car Sales...

Question 10

Solve the problem.
-The level of water in a tank after elapsed time t in minutes is given by R(t)= 6t + 1 inches. Draw a graph for this function. At what time will the water start overflowing from the tank if the depth of
The tank is 79 inches? 
A) 15 minutes;

B) 23 minutes;

C) 23 minutes;

D) 13 minutes;

Accepted Answer

The answer of Solve the problem.
-The level of water in...

Question 11

Solve the problem.
-The number of marbles y that Jack has is a function of the number of marbles x that Kevin has. This is shown in the following graph. Write an equation for y(x). 
A) $y = 5 x$
B) $y = x$
C) $y = \frac { x } { 2 }$
D) $y = 2 x$

Accepted Answer

The answer of Solve the problem.
-The number of marbles y...

Question 12

Find or investigate the function as requested.
-If water is added to an empty tank such that the water level rises by 2 cm every 25 minutes, then what is the level of the water L(t)in the tank after t minutes? 
A) $\mathrm { L } ( \mathrm { t } ) = \frac { 25 } { 2 } \mathrm { t }$
B) $L ( t ) = 2 t$
C) $\mathrm { L } ( \mathrm { t } ) = 50 \mathrm { t }$
D) $\mathrm { L } ( \mathrm { t } ) = \frac { 2 } { 25 } \mathrm { t }$

Accepted Answer

The water level rises by 2 cm every 25 minutes, so the rate of increase is $2/25$ cm per minute. Therefore, the level of the water $L(t)$ after $t$ minutes is $L(t) = \frac{2}{25}t$.

Question 13

Solve the problem.
-A plane starts its descent from a cruising altitude of 32,000 feet. It descends at a rate of 2500 feet per minute. Draw a graph in which the plane's altitude is measured on the vertical axis and use the Graph to estimate how long it will take for the plane to reach an altitude of 4000 feet. 
A) About 11 minutes
B) About 18 minutes
C) About 7 minutes

Accepted Answer

The answer of Solve the problem.
-A plane starts its descent...

Question 14

Solve the problem.
-A moving firm charges a flat fee of $30 plus $25 per hour. Find the cost C(x)of using the moving firm for x hours. 
A) $C ( x ) = 25 x + 30$
B) $C ( x ) = 25 x - 30$
C) $C ( x ) = 30 x - 25$
D) $C ( x ) = 30 x + 25$

Accepted Answer

The cost C(x) includes a flat fee of $30 plus $25 for each hour x, so the formula is $C ( x ) = 25 x + 30$.

Question 15

Find or investigate the function as requested.
-If  t(n)  represents the nth term of a sequence for $\mathrm { n } \in \mathrm { N }$ and  t(n)=4 n+2 , then is 33 a value of the function whose domain is N?
A) Yes
B) No

Accepted Answer

The function t(n) = 4n + 2 produces even numbers only, since both 4n (for any integer n) and 2 are even. The number 33 is odd, so it cannot be produced by this function.

Question 16

Solve the problem.
-Given the table below, find the rule for output given that n is the input. $\begin{array}{r|rrrr}
\text { Input } & 4 & 2 & 0 & -3 \
\hline \text { Output } & 17 & 5 & 1 & 10
\end{array}$

A) $f ( n ) = ( n + 1 ) ^ { 2 }$
B) $f ( n ) = 3 n + 2$
C) $f ( n ) = 2 n + 2$
D) $f ( n ) = n ^ { 2 } + 1$

Accepted Answer

The rule that fits all given input-output pairs is $f(n) = n^2 + 1$, as squaring the input and adding 1 matches the output for all provided inputs.

Question 17

Solve the problem.
-A house was purchased for $79,000. After 9 years the value of the house was $106,000. Express the house's value V(t)in terms of time t in years.
A)V(t)= 9t + 79,000
B)V(t)= 3000t
C)V(t)= 3000t + 79,000
D)V(t)= 106,000

Accepted Answer

The house's value increased by $27,000 over 9 years, which is a rate of $3,000 per year. Therefore, the value V(t) = initial value + rate of increase * time, or V(t) = 79,000 + 3000t.

Question 18

Solve the problem.
-The fixed cost for producing an item is $430. 10 items cost $1610 to produce. Express the total cost C(x)in terms of x, the number of items produced.
A)C(x)= 236x + 430
B)C(x)= 118x + 430
C)C(x)= 118x + 1610
D)C(x)= 236x + 1610

Accepted Answer

The total cost for producing 10 items is $1610, which includes the fixed cost of $430. The variable cost for producing 10 items is $1610 - $430 = $1180. The cost per item is $1180 / 10 = $118. Therefore, the total cost C(x) is the fixed cost plus $118 times the number of items, or C(x) = 118x + 430.

Question 19

Solve the problem.
-A company can make 12 airplane engines for $57,600, while 30 airplane engines cost $68,580. What is the cost y(x)of producing x airplane engines.
A)y(x)= 610x + 50,280
B)y(x)= 18x + 10,980
C)y(x)= 610x - 50,280
D)y(x)= x + 10,980

Accepted Answer

The cost function y(x) can be determined by finding the slope (cost per engine) and the y-intercept (fixed cost). The slope is found by the change in cost divided by the change in the number of engines: (68,580 - 57,600) / (30 - 12) = 10,980 / 18 = 610. This means each engine adds $610 to the total cost. To find the y-intercept, substitute one of the points into the equation y = 610x + b and solve for b: 57,600 = 610(12) + b, leading to b = 50,280. Therefore, the cost function is y(x) = 610x + 50,280.

Question 20

Solve the problem.
-Crafty Bill's Cool Car Sales opened as a used car sales lot in 2006. The graph shows the number of cars sold as a function of time. What is the approximate number of cars sold in 2008? 
A)500
B)250
C)600
D)650

Accepted Answer

The answer of Solve the problem.
-Crafty Bill's Cool Car Sales...

Quiz 8: Real Numbers and Algebraic Thinking

Find or investigate the function as requested. -Find a function f(n) whose domain is the set of natural numbers and the output produces the terms of the sequence 4, 16, 64, 256, . . .

Solve the problem. -John is paid a weekly salary of $380 plus 4% of his sales. Draw a graph in which sales are measured on the horizontal axis and wages on the vertical axis. Then use the graph to estimate John's sales if his week's pay is $530.

Find or investigate the function as requested. -If t(n) represents the nth term of a sequence for $\mathrm { n } \in \mathrm { N }$ and $t ( n ) = n ^ { 2 } + 2 n + 5$ , then is 29 a value of the function whose domain is N ?

Solve the problem. -The town of Appleville recorded the following dates and populations. Draw a graph of the population as a function of time. What was the approximate population of Appleville in 2002?

Find or investigate the function as requested. -Find a function f(n) whose domain is the set of natural numbers and the output produces the terms of the sequence 8, 11, 14, 17, . . .

Find or investigate the function as requested. -Find a function f(n) whose domain is the set of natural numbers and the output produces the terms of the sequence 1, 6, 11, 16, . . .

Solve the problem. -Crafty Bill's Cool Car Sales opened as a used car sales lot in 2006. The graph shows the number of cars sold as a function of time. What is the approximate number of cars sold in 2010?

Solve the problem. -The level of water in a tank after elapsed time t in minutes is given by R(t) = 6t + 1 inches. Draw a graph for this function. At what time will the water start overflowing from the tank if the depth of The tank is 79 inches?

Find or investigate the function as requested. -If water is added to an empty tank such that the water level rises by 2 cm every 25 minutes, then what is the level of the water L(t) in the tank after t minutes?

Solve the problem. -A moving firm charges a flat fee of $30 plus $25 per hour. Find the cost C(x) of using the moving firm for x hours.

Find or investigate the function as requested. -If t(n) represents the nth term of a sequence for $\mathrm { n } \in \mathrm { N }$ and t(n) =4 n+2 , then is 33 a value of the function whose domain is N?

Solve the problem. -Given the table below, find the rule for output given that n is the input. $\begin{array}{r|rrrr}\text { Input } & 4 & 2 & 0 & -3 \\\hline \text { Output } & 17 & 5 & 1 & 10\end{array}$

Solve the problem. -A house was purchased for $79,000. After 9 years the value of the house was $106,000. Express the house's value V(t) in terms of time t in years.

Solve the problem. -The fixed cost for producing an item is $430. 10 items cost $1610 to produce. Express the total cost C(x) in terms of x, the number of items produced.

Solve the problem. -A company can make 12 airplane engines for $57,600, while 30 airplane engines cost $68,580. What is the cost y(x) of producing x airplane engines.

Solve the problem. -Crafty Bill's Cool Car Sales opened as a used car sales lot in 2006. The graph shows the number of cars sold as a function of time. What is the approximate number of cars sold in 2008?