Free Printable Unit 5 Study guide spring

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?

a)

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

b)

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

c)

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

d)

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

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?

a)

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

b)

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

c)

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

d)

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

3.

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

a)

300

b)

1.16

c)

.16

d)

x

4.

Write the exponential equation

a)

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

b)

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

c)

$y=2^x$

d)

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

5.

Match the following

final value

initial value

rate

time

6.

What is the initial value from the table?

(hint: look for the y-intercept value)

a)

80

b)

40

c)

20

d)

10

e)

0

7.

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?)

a)

48 bacteria

b)

2

c)

1 day

d)

24 hours

8.

Match rate when written as a % and decimal

3%

0.03

50%

0.30

30%

0.05

5%

0.50

9.

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.

a)

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

b)

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

c)

$y=9x+3$

d)

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

e)

Neither function

10.

What is the y-intercept?

a)

(0,0)

b)

(0,1)

c)

(-3,0)

d)

(0,-3)

11.

In an exponential function, what does the 'a' represent?

En una función exponencial, ¿qué representa la 'a'?

a)

Slope

Pendiente

b)

Rate of change

Tasa de cambio

c)

Y-intercept

Intersección en Y

d)

Multiplier

Multiplicador

e)

I don't know

No sé

12.

What is the Y-intercept? A=______

What is the Ratio? B=_____

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

a)

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

b)

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

c)

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

d)

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

13.

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?

a)

$9,004.07

b)

$2,2848.80

c)

$9,011.94

d)

$8,242.71

14.

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

a)

$5,884.00

b)

$5,178.97

c)

$2,992.96

d)

$2,957.04

15.

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?

a)

b)

c)

d)

16.

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

a)

The population will be 225,000.

b)

The population will be 450,000.

c)

The population will be 900,000.

d)

The population will be 1,800,000.

17.

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

a)

between 1 and two years

b)

more than 5 years

c)

less than a year

d)

between 3 and 4 years

18.

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?

a)

19 to 20 hours

b)

10 to 20 hours

c)

15 to 16 hours

d)

5 to 6 hours

19.

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.

a)

y=1400(1.09)^x

b)

y=1.09(1400)^x

c)

y=1400(.91)^x

d)

y=1.09^x

20.

Name the asymptote.

a)

x = -4

b)

y = -5

c)

y = -4

d)

x = -5

21.

Name the range.

a)

x> -4

b)

y > -5

c)

y < -4

d)

x < -5

22.

Name the range.

a)

y> 1

b)

y >2

c)

y < 2

d)

y < 1

23.

Name the domain.

a)

x> -2

b)

y > -3

c)

y < -3

d)

all real numbers

24.

Label the transformations of $y=x^2$ shown.

H. Shift Right 5

H. Reflection

V. Shift Down 5

V. Reflection

V. Shift Up 2

H. Shift Left 2

H. Shift RIght 2

d

f

c

c)

d)

f)

25.

What is the horizontal asymptote for the graph of

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

a)

y=0.5

b)

y=13

c)

y=6

d)

y=0

26.

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

a)

b)

c)

d)

27.

Select the two end behaviors.

a)

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

b)

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

c)

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

d)

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

28.

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?

a)

198

b)

170

c)

105

d)

110

29.

What is the End behavior on the right side

a)

x→∞, y→∞

b)

x→⁻∞, y→∞

c)

x→⁻∞, y→0

d)

x→∞, y→⁻∞

30.

Find the average rate of change over the given interval.

a)

4

b)

7

c)

7/3

d)

3/7

31.

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.

a)

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

b)

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

c)

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

d)

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

32.

Who has the greater rate of change?

a)

Smith has the greater rate of change with 5/4

b)

Harmon has the greater rate of change with 7/2

c)

Smith has the greater rate of change with 4/5

d)

They have the same rate of change.

33.

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

a)

72

b)

3

c)

36.8

d)

630

34.

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

a)

Domain: All Real Numbers

Range: All Real Numbers

b)

Domain: All Real Numbers

Range: y < 2

c)

Domain: All Real Numbers

Range: y > 2

d)

Domain: x > 2

Range: All Real Numbers

35.

Match the following

Growth

$y\ =\ ab^x$

Decay

y-intercept

b

Exponential Function Equation

a

Growth/Decay Factor

36.

Describe the translation.

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

a)

Up 2

b)

Down 2

37.

Describe the translation.

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

a)

Up 3

b)

Down 3

38.

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

a)

16, 19, 22

b)

17, 19, 21

c)

17, 20, 23

d)

16, 18, 20

39.

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

a)

155

b)

135

c)

132

d)

75

40.

Which is the graph of

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

a)

b)

c)

d)

41.

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

a)

a_n=12+3n

b)

a_n=25+13n

c)

a_n=13n+12

d)

a_n=12-5n

42.

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

a)

a_n = a_n-1 x 3

b)

a_n = 5(3)^n-1

c)

a_n = 3(5)^n-1

d)

a_n = 5 + (n-1)3

43.

Write the explicit formula for the geometric sequence.

a)

a_n = 4(3)^n-1

b)

a_n = 3(4)^n-1

c)

a_n = -4(3)^n-1

d)

a_n = 3(-4)^n-1

44.

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

a_1=6

a_n=5\cdot a_{n-1}

a)

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

b)

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

c)

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

d)

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

45.

Write the explicit formula for the following geometric sequence:

10, 20, 40, 80, ...

a)

a_n = 10(2)^n-1

b)

a_n = 2(10)^n-1

c)

a_n = 10(2)ⁿ

d)

a_n = 2(10)ⁿ

46.

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

a)

17

b)

27

c)

-7

d)

23

47.

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

a)

8

b)

4

c)

2

d)

Cannot be determined

Unit 5 Study guide spring

Total questions: 47

Worksheet time: 2hrs 4mins

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