Quiz about Unit 6 Review

Question 1

Which of the following sequences demonstrates exponential growth?

Accepted Answer

2, 4, 8, 16

Answer

3, 6, 9, 12

Answer

7, 14, 21, 28

Answer

10, 20, 30, 40

Question 2

Which expression below is equivalent to the following?

$$\left(3^{2x+1^{ }}\right)\left(\ 3^{x-1}\right)$$

Accepted Answer

$$3^{3x}$$

Answer

$$3^{2x+2}$$

Answer

$$3^{3x+2}$$

Answer

$$3^{x+2}$$

Question 3

When the fraction $$\frac{5x^6}{15x^9}$$ is simplified it can be written as which of the following?

Accepted Answer

$$\frac{1}{3x^3}$$

Answer

$$\frac{x^3}{3}$$

Answer

$$3x^3$$

Answer

$$\frac{x^3}{5}$$

Question 4

If $$g\left(x\right)=4\left(2\right)^x$$ then which of the following is the value of g(-3)?

Accepted Answer

$$\frac{1}{2}$$

Answer

$$-\frac{1}{2}$$

Answer

$$\frac{1}{8}$$

Answer

-32

Question 5

Which of the following equations could represent the graph of the red function shown?

Accepted Answer

$$y=6\left(1.1\right)^x$$

Answer

y = 2x - 3

Answer

$$y=5\left(0.75\right)^x$$

Answer

$$y=3\left(0.9\right)^x$$

Question 6

Which expression below is equivalent to $$\frac{9^{x+1}}{27}$$ ?

Accepted Answer

$$3^{2x-1}$$

Answer

$$\left(\frac{1}{3}\right)^{x+1}$$

Answer

$$\left(\frac{1}{9}\right)^{x+1}$$

Answer

$$9^{x-1}$$

Question 7

Maria's monthly gym membership fee is $80. Next month, the fee will increase by 7%. What will be her new monthly fee after the increase?

Accepted Answer

$85.60

Answer

$84.00

Answer

$86.40

Answer

$88.00

Question 8

An exponential function of the form $ y = a(b)^x $ passes through the points (1, 3) and (3, 12). Which of the following is closest to the value of b for this function?

Accepted Answer

b = 2.00

Answer

b = 1.50

Answer

b = 1.75

Answer

b = 2.25

Question 9

In a controlled environment, researchers are observing the growth of a bacterial colony. They represent the colony's population with the function $$n\left(t\right)=50\left(1.075\right)^t$$ , where t is the number of hours since the observation began. Explain the significance of the parameters 50 and 1.075 in this context.

Accepted Answer

50 is the initial number of bacteria in the colony

1.075 indicates that the bacteria are growing at a rate of 7.5% per hour.

Answer

50 is the initial number of bacteria in the colony

1.075 indicates that the bacteria are decreasing at a rate of 7.5% per hour.

Answer

50 is the initial number of bacteria in the colony

1.075 indicates that the bacteria are growing at a rate of 75% per hour.

Answer

50 is the initial number of bacteria in the colony

1.075 indicates that the bacteria are decreasing at a rate of 0.75% per hour.

Question 10

The number of research papers in Professor Sycamore area of expertise has been increasing by 5% every year. Given that 30,010 research papers were published this year. Assuming the trend continues, which equation projects the amount of research papers published in x years?

Accepted Answer

y = 30,010 (1.05)^x

Answer

y = 30,010 (.05)^x

Answer

y = 30,010 (.95)^x

Answer

y = 30,010 (5)^x

Question 11

This is an example of.....

Accepted Answer

exponential decay

Answer

exponential growth

Answer

constant change

Answer

a linear function

Question 12

Determine the population for year 3 of the table.

Accepted Answer

8.64

Answer

8.2

Answer

8.4

Answer

9

Question 13

What is the simplified form of the expression $$\frac{12x^5}{4x^2}$$ ?

Accepted Answer

$$3x^3$$

Answer

$$\frac{1}{3x^3}$$

Answer

$$\frac{3}{x^3}$$

Answer

$$3x^2$$

Question 14

Which of the following sequences demonstrates exponential decay?

Accepted Answer

100, 50, 25, 12.5

Answer

5, 10, 20, 40

Answer

1, 2, 3, 4

Answer

8, 16, 32, 64

Question 15

If $$f\left(x\right)=5\left(3\right)^x$$ , what is the value of f(2)?

Accepted Answer

45

Answer

90

Answer

25

Answer

15

Unit 6 Review

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