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Assessment: Lesson 6-1 and 6-2

Total questions: 79

Worksheet time: 6hrs 56mins

Name
Class
Date
1.

Select the equations that show exponential growth.

a)

f(x) =3(1.01)xf\left(x\right)\ =3\left(1.01\right)^x  

b)

f(x)=4000(0.95)x+1f\left(x\right)=4000\left(0.95\right)^{x+1}  

c)

f(x)=4xf\left(x\right)=4^x  

d)

f(x)= 0.5(3)xf\left(x\right)=\ 0.5\left(3\right)^x  

e)

f(x)=25(0.25)xf\left(x\right)=25\left(0.25\right)^x  

2.

Select the equations that show exponential decay.

a)

f(x) =3(1.01)xf\left(x\right)\ =3\left(1.01\right)^x  

b)

f(x)=4000(0.95)x+1f\left(x\right)=4000\left(0.95\right)^{x+1}  

c)

f(x)=4xf\left(x\right)=4^x  

d)

f(x)= 0.5(3)xf\left(x\right)=\ 0.5\left(3\right)^x  

e)

f(x)=25(0.25)xf\left(x\right)=25\left(0.25\right)^x  

3.

A population of 1500 deer decreases by 1.5% per year. At the end of 10 years, there will be approximately 1290 deer in the population. Which function can be used to determine the number of deer, y, in this population at the end of t years?

a)

y= 1500(0.985)ty=\ 1500\left(0.985\right)^t

b)

y= 1500(0.015)ty=\ 1500\left(0.015\right)^t

c)

y= 1500(1.015)ty=\ 1500\left(1.015\right)^t

d)

y= 1500(1.5)ty=\ 1500\left(1.5\right)^t

4.
There were 417 cell phones sold at an electronics store in January. Since then, cell phone sales at this store have increased at a rate of 3.75% per month. At this rate of growth, which function can be used to determine the monthly cell phone sales x months after January?
a)
f(x) = 417(3.75)x
b)
f(x) = 417(0.0375)x
c)
f(x) = 417(1.0375)x
d)
f(x) = 417(1.375)x
5.
Some banks charge a fee for a savings account that is left inactive for an extended period of time. The equation y = 5000(0.98)x represents the amount remaining, y, of one account that was left inactive for a period of x years. What does the number 5000 represent in this situation?
a)
A fee charged for an inactive account
b)
The percent of money in the account after x years
c)
The amount of money in the account initially
d)
The amount of money in the account after x years
6.
a)

f(x) = 25(0.95)x

b)

f(x) = 36(0.05)x

c)

f(x) = 25(1.05)x

d)

f(x) = 36(1.5)x

7.
A child asks her dad for an allowance that starts with a penny and then doubles every day for a month. Which function can be used to model the amount of money, A, the child will receive each day, x?
a)
A(x) = 2(0.01)x
b)
A(x) = 0.01(2)x
c)
A(x) = 0.01(1 - 2)x
d)
A(x) = 2(1.01)x
8.
The function to find the value of a car after t years is given by v(t) = 24,000(.75)t Which of the following statements is not true?
a)
The starting value of the car was $24,000.
b)
The y-values of the graph increase as the x-values increase.
c)
The value of b indicates this is an exponential decay situation.
d)
The horizontal asymptote is y = 0, which means the car will never have a value of $0.
9.
A population of fish starts at 8,000 and decreases by 6% per year. What is the population of fish after 10 years?
a)
14327
b)
4309
c)
839
d)
7680
10.
Daniel’s Print Shop purchased a new printer for $35,000. Each year it depreciates at a rate of 5%. How much will the printer be worth in 8 years?
a)
$23,219.72
b)
$136.72
c)
$51,710.94
d)
$16,710.94
11.

What is the initial value for the function: f(x) = 300(1.16)x?

a)

300

b)

1.16

c)

.16

d)

x

12.
Write an equation that models the following situation:
Samantha's hair was known to grow very rapidly. It began at a length of 6 in and grew at a rate of 14% a week.
a)
y=6(0.14)x
b)
y=6(1+14)x
c)
y=6(1.14)x
d)
y=6(0.86)x
13.
Suppose a culture of bacteria begins with 5000 cells and dies by 30% each year. Write an equation that represents this situation.
a)
y=5000(0.7)x
b)
y=30(5000)x
c)
y=5000(1.3)x
d)
y=5000xx
14.

What is the range of this graph?

a)

y = 6

b)

(0, -3)

c)

y > -4

d)

y < -4

15.
What is the y-intercept of the function?
a)
2
b)
3
c)
1
d)
-2
16.
Suppose you deposit $3000 in a savings account that pays interest at an annual rate of 4%.  What is the initial value?
a)
4%
b)
40%
c)
$3000(1.04)
d)
$3000
17.

What is the y-intercept?

a)

5

b)

1/3

c)

1

d)

0

18.

Which of the following statement about the graph of y=6(.5)x is true?

a)

The equation of the asymptote is x=0.

b)

The coordinates of the y-intercept are (0,6)

c)

The graph includes the point (1.5, 2).

d)

The coordinates of the x-intercept are (.75, 0)

19.

Based on the graph, which statement does not appear to be true?

a)

The graph has a horizontal asymptote at y=0

b)

The y-intercept is at the point (0, 3)

c)

The graph represents exponential growth.

d)

The graph of the function shows a decrease over time.

20.
You borrowed $59,000 for 2 years at 11% which was compounded annually.  What total will you pay back?
a)
$13,693.90
b)
$1,363.90
c)
$72,693.90
d)
$73,793.90
21.
Semi-Annually means how many times a year?
a)
4 
b)
2
c)
1
d)
6
22.
Riley invested $1,000 in savings bonds. If the bonds earn 6.75% interest compounded semi-annually, how much total will Riley earn in 15 years?
a)
$1,584.62
b)
$2,651.39
c)
$2,706.86
d)
$1,825.10
23.
Olivia would like to buy some new furniture for her home. She decides to buy the furniture on credit with 9.5% interest compounded quarterly. If she spent $7,400, how much total will she have paid after 8 years.
a)
$15,415.94
b)
$15,683.28
c)
$15,927.56
d)
$16,109.05
24.
Approximately what interest rate would be needed in order to grow an investment of $1,400 to $2,500 in 10 years if the interest was compound monthly?
a)
5.96%
b)
5.84%
c)
5.81%
d)
5.88%
25.
Given an investment of $1,500:
Which investment would have a larger balance after 5 years?
Option 1 - 4% compounded monthly
Option 2 - 3.9% compounded daily. 
a)
Option 1
b)
Option 2
26.

Caiden earned $475 from mowing lawns last summer.He deposited this money in an account that pays an interest rate of 3.8% compounded annually. What will be his balance after 15 years?

a)

$827.52

b)

$831.10

c)

$839.45

d)

$846.80

27.

What does the P stand for in this formula?

a)

Initial amount

b)

Final amount

c)

Rate

d)

Time

e)

The number of times compounded per year

28.

What does the n stand for in this formula?

a)

Initial amount

b)

Final amount

c)

Rate

d)

Time

e)

The number of times compounded per year

29.

Maggie would like to buy some new furniture for her home. She decides to buy the furniture on credit with 9.5% interest compounded quarterly. If she spent $7,400, how much total will she have paid after 8 years?

a)

$15,415.94

b)

$15,683.28

c)

$15,927.56

d)

$16,109.05

30.

Approximately what interest rate would be needed in order to grow Christian's investment of $1400 to $2500 in 10 years if the interest was compound monthly?

a)

5.96%

b)

5.84%

c)

5.81%

d)

5.88%

31.

Treasure won $3,000 from a radio contest. If she puts this money in a bank account that earns 2.9% interest compounded quarterly, how much total will she earn in 10 years?

a)

$4915.59

b)

$3933.28

c)

$2979.81

d)

$4005.09

32.
What is the formula for continuously compounded interest?
a)
A = Pert
b)
A = Pet
33.

Cora invested $400 at a rate of 35% for 8 months, compounded continuously. How much is her investment worth after 8 months?

a)

$520.07

b)

$505.12

c)

$460.11

d)

$7,643.74

34.

How long will it take $3000 to double if it is invested in an account that pays 3% compounded continuously?

a)

23.1 years

b)

22.1 years

c)

21.1 years

d)

20.1 years

35.
If $1,000 is invested at 16% interest, compounded continuously, for five years, what is the ending balance?
a)
$1,225,54
b)
$2,225.54
c)
$22,255.40
d)
$225.54
36.
Andy invests $500 into an account with 4.8% interest, compounded monthly. How much will be in the account in 10 years?
a)

$799.06

b)

$520.36

c)

$807.26

d)

$877.61

37.
Mr. T invested $15,000 in an account that pays 5% interest compounding continuously, how much is in the account after 5 years? 
a)
$15,500.50
b)
$19,260.38
c)
$19,260.40
d)
$21,500.25
38.
P = 26,000 | Rate = 2.4% | 4 years | Compounded Continuously | Amount owed???
a)
$2,496
b)
$28,496
c)
$3,406,924
d)
$28,619.74
39.
How much money will you have in 3 years if you invest $1025 in an account with 12% interest compounded continuously?
a)
$1114.76
b)
$1302.67
c)
$1392.45
d)
$1469.16
40.
Which of the following functions shows an initial amount of $15 and an increase of 35% each year?
a)
y = 15(35)x
b)
y = 15(1.35)x
c)
y = 15(0.35)x
d)
y = 35(1.15)x
41.
Is the pictured graph growth, decay, or linear or none?  
a)
Exponential Growth
b)
Exponential Decay
c)
Linear
d)
None
42.
Is this exponential growth or decay?
a)
Growth
b)
Decay
43.
Write an equation that models the following situation:
Samantha's hair was known to grow very rapidly. It began at a length of 6 in and grew at a rate of 14% a week.
a)
y=6(0.14)x
b)
y=6(1+14)x
c)
y=6(1.14)x
d)
y=6(0.86)x
44.
A population of fish starts at 8,000 and decreases by 6% per year. What is the population of fish after 10 years?
a)
14327
b)
4309
c)
839
d)
7680
45.
Daniel’s Print Shop purchased a new printer for $35,000. Each year it depreciates at a rate of 5%. How much will the printer be worth in 8 years?
a)
$23,219.72
b)
$136.72
c)
$51,710.94
d)
$16,710.94
46.
The number of mosquitoes at the beginning of the summer was 4,000. The population of mosquitoes is expected to grow at a rate of 25% a month. How many mosquitoes will there be after 4 months?
a)
9766
b)
9006
c)
9765
d)
5433
47.
Twenty years ago, Mr. Davis purchased his home for $160,000. Since then, the value of the home has increased about 5% per year. How much is the home worth today?
a)
$176,783.29
b)
$424,527.63
c)
$57,357.75
d)
$532,041,076.80
48.
A stamp gets more expensive each year.  It increases in value by 60 % each year.  What is the growth FACTOR?
a)
.6
b)
1.06
c)
1.6
d)
.4
49.
Suppose you deposit $3000 in a savings account that pays interest at an annual rate of 4%.  What is the growth factor?
a)
.96
b)
1.4
c)
1.04
d)
$3000
50.
Which of the following functions shows an initial amount of $15 and an increase of 35% each year?
a)
y = 15(35)x
b)
y = 15(1.35)x
c)
y = 15(0.35)x
d)
y = 35(1.15)x
51.
Daniel’s Print Shop purchased a new printer for $35,000. Each year it depreciates at a rate of 5%. How much will the printer be worth in 8 years?
a)
$23,219.72
b)
$136.72
c)
$51,710.94
d)
$16,710.94
52.
Since January 1980, the population of the city of Brownville has grown according to the mathematical model y=720,500(1.022)x, where x is the number of years since January 1980. What is the was the population of Brownville in 1980?
a)
102.2 people
b)
720,500 people
c)
1.022 people
d)
1022 people
53.
Suppose you deposit $3000 in a savings account that pays interest at an annual rate of 4%. If no other money is added or withdrawn from the account, how much will be in the account after 10 years?
a)
$3122.18
b)
$4994.50
c)
$4440.73
d)
$86,776.40
54.
The attendance at the art museum at the New Year’s opening was 250 people. The attendance has been increasing at a rate of 3% each month. How many people will attend by the end of a year?
a)
356
b)
265
c)
5825
d)
1329
55.
In 1985, there were 285 cell phone subscribers in the small town of Centerville. The number of subscribers increased by 75% per year after 1985. How many cell phone subscribers were in Centerville in 1994?
a)
OVERFLOW
b)
1994
c)
1000
d)
43871
56.
You buy a new computer for $2100. The computer decreases by 50% annually. How much is it worth after 2 years.
a)
225
b)
325
c)
425
d)
525
57.
The population of Bloom Falls, Mass. (population 937) is slowly moving to a bigger city.
Every year the population drops by 4.5%. What is the population after 3 years?
a)
1,069 people
b)
894 people
c)
816 people
d)
854 people
58.

The city of Whoville has been much more stable since the Grinch turned his life around. The population of 900 is increasing at a rate of 7.5% per year. If the population continues growing at the same rate, how many people will there be in 11 years?

a)

424288

b)

1994

c)

10642

d)

900

59.

The Country of Puerto has 3,370,000 people in it and is decreasing at a rate of 4.5%. Estimate the population after 40 years.

a)

534,275

b)

19,601,148

c)

1,350,756

d)

2,521,541

60.
If $1,000 is invested at 16% interest, compounded continuously, for five years, what is the ending balance?
a)
$1,225,54
b)
$2,225.54
c)
$22,255.40
d)
$225.54
61.
Change 32% into a decimal.
a)
32
b)
3.2
c)
.32
d)
.032
62.
Convert 70% to a decimal.
a)
.07
b)
.70
c)
.007
d)
.01
63.
Convert 3% to a decimal.
a)
.03
b)
.30
c)
.05
d)
.06
64.
Convert 3.5% to a decimal.
a)
3.5
b)
350
c)
.35
d)
.035
65.
Mr. T invested $15,000 in an account that pays 5% interest compounding continuously, how much is in the account after 5 years? 
a)
$15,500.50
b)
$19,260.38
c)
$19,260.40
d)
$21,500.25
66.

How long would it take $7,000 to grow to $35,000 at 6% compounded continuously?

a)

27.6 years

b)

27.1 years

c)

26.0 years

d)

26.9 years

67.

Chelsea put $7500 into an account paying 5% compounded continuously. She now has $10,643.01. How long has the money been in the account?

a)

7 years

b)

6 years

c)

5 years

d)

4 years

68.

What does the A stand for in this formula?

a)

Initial Amount

b)

Final Amount

c)

Rate

d)

Time

e)

The number of times compounded per year

69.

What does the P stand for in this formula?

a)

Initial amount

b)

Final amount

c)

Rate

d)

Time

e)

The number of times compounded per year.

70.

Which formula is shown?

a)

Monthly compounded interest formula

b)

Annually compounded interest formula

c)

Continuously compounded interest formula

d)

Simple interest formula

71.

What does the r stand for in this formula?

a)

Rate as a percent

b)

Rate as a decimal

c)

number of times interest is compounded

72.

What does the t stand for in this formula?

a)

time in weeks

b)

time in months

c)

time in years

d)

the number of times interest is compounded per year

73.
When would we use this formula? A = Pe rt
a)
interest increases by fixed amount
b)
compound interest 
c)
compound continuously 
d)
decreases by fixed percent
74.

A student solves a problem about continuously compounded interest and determines that r = .3

a)

They should conclude that the interest rate is .3%

b)

They should conclude that the interest rate is 3%

c)

They should conclude that the interest rate is 30%

d)

They should conclude that the interest compounded for .3 years

75.
If $1,000 is invested at 16% interest, compounded continuously, for five years, what is the ending balance?
a)
$1,225,54
b)
$2,225.54
c)
$22,255.40
d)
$225.54
76.
If $1,000 is invested at 16% interest, compounded continuously, for five years, what is the ending balance?
a)
$1,225,54
b)
$2,225.54
c)
$22,255.40
d)
$225.54
77.

Mr. Thomas invested $15,000 in an account that pays 5% interest compounding continuously, how much is in the account after 5 years?

a)

$15,500.50

b)

$19,260.38

c)

$19,260.40

d)

$21,500.25

78.

If You Compounded Continuously an investment of $400 at a rate of 35% for 2 years

a)

$280

b)

$680

c)

$1,034.47

d)

$805.50

79.

Caiden earned $475 from mowing lawns last summer. He deposited this money in an account that pays an interest rate of 3.8% compounded continuously. What will be his balance after 15 year?

a)

$827.52

b)

$839.93

c)

$839.45

d)

$846.80

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