Quiz about Unit 5 Study guide spring

Question 1

A chiropterologist is a scientist who studies bats. A bat colony is discovered and a chiropterologist calculates that there are 2,100 bats in the colony. If the population of the colony doubles each year, which function, B(t), describes the population of the colony t years after discovery?

Accepted Answer

$$B\left(t\right)=2100\left(2\right)^t$$

Answer

$$B\left(t\right)=2100\left(\frac{1}{2}\right)^t$$

Answer

$$B\left(t\right)=2100+\left(2\right)^t$$

Answer

$$B\left(t\right)=2100+\left(\frac{1}{2}\right)^t$$

Question 2

Chris purchased a used truck for $11,500. According to an online vehicle website, his truck will depreciate, or lose value, at a rate of 5.5% each year. What function, d(x), represents the value of Chris's truck x years after its purchase?

Accepted Answer

$$d\left(x\right)=11,500\left(0.945\right)^x$$

Answer

$$d\left(x\right)=11,500\left(1.055\right)^x$$

Answer

$$d\left(x\right)=11,500\left(0.055\right)^x$$

Answer

$$d\left(x\right)=11,500\left(5.5\right)^x$$

Question 3

What is a, the starting term, for the function: f(x) = 300(1.16)^x?

Accepted Answer

300

Answer

1.16

Answer

.16

Answer

x

Question 4

Write the exponential equation

Accepted Answer

$$y=2\left(2\right)^x$$

Answer

$$y=4\left(2\right)^x$$

Answer

$$y=2^x$$

Answer

$$y=2\left(4\right)^x$$

Question 5

What is the initial value from the table?

(hint: look for the y-intercept value)

Accepted Answer

20

Answer

80

Answer

40

Answer

10

Answer

0

Question 6

A Petri dish currently has 48 bacteria. Each hour, the total number doubles. The bacteria are allowed to grow for one full day.

(What is the rate?)

Accepted Answer

2

Answer

48 bacteria

Answer

1 day

Answer

24 hours

Question 7

Determine if each table of values represents a linear function, exponential function or neither function.

If it does represent a linear or exponential function, write an equation to model the table of values.

Accepted Answer

$$y=9\left(\frac{1}{3}\right)^x$$

Answer

$$y=27\left(3\right)^x$$

Answer

$$y=9x+3$$

Answer

$$y=\frac{1}{3}x+27$$

Answer

Neither function

Question 8

What is the y-intercept?

Accepted Answer

(0,-3)

Answer

(0,0)

Answer

(0,1)

Answer

(-3,0)

Question 9

What is the Y-intercept? A=______

What is the Ratio? B=_____

What is the Exponential Equation? f(x)=_____________

Accepted Answer

A=2; B=4 $$f\left(x\right)=2\cdot4^x$$

Answer

A=2; B=4 $$f\left(x\right)=4\cdot2^x$$

Answer

A=2; B=4 $$f\left(x\right)=8^x$$

Answer

A=2; B=6 $$f\left(x\right)=2+6^x$$

Question 10

Ash has $8,000 in a savings account. The interest rate is 3% compounded once a year.

To the nearest cent, how much will he have in his account in 4 years?

Accepted Answer

$9,004.07

Answer

$2,2848.80

Answer

$9,011.94

Answer

$8,242.71

Question 11

A sailboat that costs $5,950 decreases in value by 11% per year. How much will the boat be worth after 6 years?

Accepted Answer

$2,957.04

Answer

$5,884.00

Answer

$5,178.97

Answer

$2,992.96

Question 12

Katy deposited $90 in a savings account earning 5% interest, compounded quarterly. Which of the following equations could represent the amount of money in her account yearly?

Accepted Answer

Option D is correct

Answer

A.

Answer

B.

Answer

C.

Question 13

A city doubles its size every 64 years. If the population is currently 225,000, what will the population be in 128 years?

Accepted Answer

The population will be 900,000.

Answer

The population will be 225,000.

Answer

The population will be 450,000.

Answer

The population will be 1,800,000.

Question 14

You buy a new computer for $2100. The computer decreases by 50% annually. When will the computer have a value of $600?

Accepted Answer

between 1 and two years

Answer

more than 5 years

Answer

less than a year

Answer

between 3 and 4 years

Question 15

You drink a beverage with 120 mg of caffeine. Each hour, the caffeine in your system decreases by about 12%. How long until you have 10mg of caffeine?

Accepted Answer

19 to 20 hours

Answer

10 to 20 hours

Answer

15 to 16 hours

Answer

5 to 6 hours

Question 16

The original value of a painting is $1400, and the value increases by 9% each year. Write an exponential growth function to model this situation.

Accepted Answer

y=1400(1.09)^x

Answer

y=1.09(1400)^x

Answer

y=1400(.91)^x

Answer

y=1.09x

Question 17

Name the asymptote.

Accepted Answer

y = -5

Answer

x = -4

Answer

y = -4

Answer

x = -5

Question 18

Name the range.

Accepted Answer

y > -5

Answer

x> -4

Answer

y < -4

Answer

x < -5

Question 19

Name the range.

Accepted Answer

y> 1

Answer

y >2

Answer

y < 2

Answer

y < 1

Question 20

Name the domain.

Accepted Answer

all real numbers

Answer

x> -2

Answer

y > -3

Answer

y < -3

Question 21

What is the horizontal asymptote for the graph of

f(x)=13(0.5)^x?

Accepted Answer

y=0

Answer

y=0.5

Answer

y=13

Answer

y=6

Question 22

Which is the best graph for $$f\left(x\right)=-3^x$$ ?

Accepted Answer

Option C is correct

Answer

A.

Answer

B.

Answer

D.

Question 23

Select the two end behaviors.

Accepted Answer

As $$x\rightarrow-\infty,y\rightarrow\infty$$ .

Accepted Answer

As $$x\rightarrow\infty,\ y\rightarrow0$$ .

Answer

As $$x\rightarrow-\infty,\ y\rightarrow0$$ .

Answer

As $$x\rightarrow\infty,\ y\rightarrow\infty$$ .

Question 24

The equation

$$y=100\left(1.05\right)^t$$ represents the number of flies in an experiment, where y is the total number after t days. How many flies would there be after two weeks?

Accepted Answer

198

Answer

170

Answer

105

Answer

110

Question 25

Find the average rate of change over the given interval.

Accepted Answer

7/3

Answer

4

Answer

7

Answer

3/7

Question 26

The number of decks of popular trading cards is a function f of the number of days d since the shipment arrived.

Calculate the average rate of change from day 0 to day 5.

Accepted Answer

$$\frac{1283-2000}{5\ -\ 0}=-143.4$$

Answer

$$\frac{2000-1283}{5\ -\ 0}=\ 143.4$$

Answer

$$\frac{5-0}{1283-2000}=-0.007$$

Answer

$$\frac{5-0}{2000-1283}=0.007$$

Question 27

Who has the greater rate of change?

Accepted Answer

Harmon has the greater rate of change with 7/2

Answer

Smith has the greater rate of change with 5/4

Answer

Smith has the greater rate of change with 4/5

Answer

They have the same rate of change.

Question 28

What is the average rate of change of y = 2(3)^x at [2, 4]?

Accepted Answer

72

Answer

3

Answer

36.8

Answer

630

Question 29

What are the domain and range of the function/graph?

Accepted Answer

Domain: All Real Numbers

Range: y > 2

Answer

Domain: All Real Numbers

Range: All Real Numbers

Answer

Domain: All Real Numbers

Range: y < 2

Answer

Domain: x > 2

Range: All Real Numbers

Question 30

Describe the translation.

$$y\ =\ 3^x+\ 2$$

Accepted Answer

Up 2

Answer

Down 2

Question 31

Describe the translation.

$$y\ =\ 6^x-\ 3$$

Accepted Answer

Down 3

Answer

Up 3

Question 32

Find the next three terms:
5, 8, 11, 14...

Accepted Answer

17, 20, 23

Answer

16, 19, 22

Answer

17, 19, 21

Answer

16, 18, 20

Question 33

What is the 7th term in the series? 15, 35, 55...

Accepted Answer

135

Answer

155

Answer

132

Answer

75

Question 34

Which is the graph of

$$f\left(x\right)=2\cdot3^x$$

Accepted Answer

Question 35

Create the explicit formula for the sequence:
25, 38, 51, ...
(Hint: Write your formula and then simplify it.)

Accepted Answer

an=13n+12

Answer

an=12+3n

Answer

an=25+13n

Answer

an=12-5n

Question 36

Write an explicit rule for the general term of the sequence 5, 15, 45, . . . ?

Accepted Answer

a_n = 5(3)^n-1

Answer

a_n = a_n-1 x 3

Answer

a_n = 3(5)^n-1

Answer

a_n = 5 + (n-1)3

Question 37

Write the explicit formula for the geometric sequence.

Accepted Answer

a_n = 3(-4)^n-1

Answer

a_n = 4(3)^n-1

Answer

a_n = 3(4)^n-1

Answer

a_n = -4(3)^n-1

Question 38

Given the recursive formula, write the explicit formula for the geometric sequence.

$$a_1=6$$
$$a_n=5\cdot a_{n-1}$$

Accepted Answer

$$a_n=6\cdot5^{n-1}$$

Answer

$$a_n=5\cdot6^{n-1}$$

Answer

$$a_n=6+5\left(n-1\right)$$

Answer

$$a_n=5+6\left(n-1\right)$$

Question 39

Write the explicit formula for the following geometric sequence:

10, 20, 40, 80, ...

Accepted Answer

a_n = 10(2)^n-1

Answer

a_n = 2(10)^n-1

Answer

a_n = 10(2)ⁿ

Answer

a_n = 2(10)ⁿ

Question 40

Solve for x using the same base method.
3^x-20= 27

Accepted Answer

23

Answer

17

Answer

27

Answer

-7

Question 41

To solve 8 = 2^5x+7, you would need to re-write 8 as what base?

Accepted Answer

2

Answer

8

Answer

4

Answer

Cannot be determined

Unit 5 Study guide spring

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