WorksheetsUnit6B Exponential Growth and Decay Word Problems
Total questions: 65
Worksheet time: 2hrs 51mins
A sailboat that costs $5,950 decreases in value by 11% per year. How much will the boat be worth after 6 years?
$5,884.00
$5,178.97
$2,992.96
$2,957.04
The equation y = a(1 - r)x is used for:
1/2 life
Interest
Exponential Growth
Exponential Decay
The equation y = a(1 + r)x is used for:
Exponential Growth
Exponential Decay
Half Life
Interest
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.
534,275
19,601,148
1,350,756
2,521,541
A population of a city is 422,000 and increases by 12% each year. Use an exponential function to find the population of the city after 8 years.
100,144 people
1,083,024 people
1,044,856 people
200,000 people
A=10(1.01)3
A=1200(.85)6
You put $2000 in the bank and earn interest at a 2.5% rate compounded annually. How much will you have after 15 years?
$30,758.65
$2,001.56
$2,908.85
$2,896.60
Middletown High School has student elections every year. Lately, the school has seen a 5% decrease in voting from election to election. If 910 students voted this year, how many will be expected to vote 8 years from now? (Round to the nearest whole number if necessary).
604
777
29
198
More and more people are purchasing food from farmers' markets. As a consequence, a market researcher predicts that the number of farmers' markets will increase by 15% each year. If there are 6,200 farmers' markets this year, how many will there be in 10 years? (Round to the nearest whole number if necessary).
25,082
12,937
62,000
43,511
A publishing industry report predicts that magazine subscriptions will drop by 10% each year. If this prediction is correct, then how many subscribers will a magazine with 98,000 subscribers have in 10 years? (Round to the nearest whole number if necessary).
34,170
16,348
7690
76,023
Jenny has $20 in a savings account. The interest rate is 5%, compounded annually. To the nearest cent, how much interest will she earn in 2 years?
$2.05
$45.79
$1.99
$7.51
Lauren has $90 in a savings account. The interest rate is 5%, compounded annually. To the nearest cent, how much will she have in 2 years?
$99.23
$21.98
$56.46
$9.21
A cliff overlooking Oak Grove Lake is experiencing erosion, losing elevation at a rate of 5% every millennium. The cliff's current elevation is 1,200 meters. What will its elevation be in 6 millennia? (Round to the nearest whole number if necessary).
882
465
349
975
Kelsey deposited $30 in a savings account earning 10% interest, compounded annually. To the nearest cent, how much interest will she earn in 3 years?
$9.93
$2.01
$17.60
$5.75
Thanks to its environmental initiatives, Silvergrove has cut its annual CO2 emissions by 5%. This year, the town produced 290,000 metric tons of emissions. If the downward trend continues, how much CO2 will be produced 7 years from now? (Round to the nearest whole number if necessary).
202,518
135,792
78,376
20,658
The mice population is 25,000 and is decreasing by 20% each year. What will be the mice population after 3 years?
12,800
15,777
102, 475
2,500
Your new computer cost $1500 but it depreciates in value by about 18% each year. How much will your computer be worth in 6 years? (Round to the nearest cent.)
$456.01
$556.98
$778.22
$332.63
y=3(1.5)x
Growth
Decay
Neither
y=100(5)x
Growth
Decay
Neither
Evaluate the expression f(x) = 100(0.8)x for f(3).
100
240
51.2
800
In the formula y = a(1±r)t, what does the "a" represent?
The total after the increase or decrease
The initial amount
The Rate of Change
The number of times the change has happened over time
In the formula y = a(1±r)t, what does the "t" represent?
The total after the increase or decrease
The initial amount
The Rate of Change
The number of times the change has happened over time
In the formula y = a(1±r)t, what does the "r" represent?
The total after the increase or decrease
The initial amount
The Rate of Change
The number of times the change has happened over time
If something decays at a rate of 2.5% per hour, what would "t" be over two days?
2
24
48
.025
If something changed at a rate of 3% per week, what would "t" be over a time of one year?
1
7
12
52
Given the function f(x) = 1.07x, how do you know this is an exponential function?
Because the variable is in the exponent
Because the base has a decimal in it
Because f(x) is there
Because my teacher told me
Given the function f(x) = 1.07x, how do you know the exponential function shows growth or decay?
Growth or decay is determined by the value of the base
Growth or decay is determined by the value of the exponent
Because exponential functions are always growth functions
Because exponential functions are always decay functions
Given the function f(x) = 1.07x, is this a growth or decay function?
Growth
Decay
Given the function f(x) = 0.92x, is this a growth or decay function?
Growth
Decay
Given the function f(x) = 0.92x, what is the rate of change?
.92%
9.2%
.08%
8%
Given f(x) = (1.11)18 and the rate of change is 11% every day, how much time has passed?
11 days
18 days
1.11 times 18 days
Underterminable
Given f(x) = (1.0023)36 and the rate of change is 0.23% every hour, how many minutes have passed?
36
60
2160
3600
In 1985, there were 285 cell phone subscribers in Mayville. The number of subscribers increased by 75% per year after 1985. How many subscribers were in Mayville in 2008? (Verbal Question: What word tells us this is growth or decay?)
110,845,988
111, 043,298
109,678,401
110,544,827
The population in Haywardsville is decreasing at a rate of 2.5% per year. If the population in 2000 was 28,000, what will be the expected population in 2015 if this rate of decrease continues? (Verbal Question: How do we know this is growth or decay?)
19,153
19,285
18,956
19,172
The value of a book is $58 and depreciates at a rate of 7% per year. Write an exponential function to find the value of the book after 8 years. (Verbal Question: How do we know this is growth or decay?)
f(t) = 58(0.93)t; $32.46
f(t) = 58(1.07)t; $76.32
f(t) = 58(0.93)t; $34.26
f(t) = 58(1.07)t; $73.62
The population of a small town is 1600 and is increasing at a rate of 3% per year. Write an exponential function to model this situation. Then find the population of the town after 10 years. (Verbal Question: How do we know this is growth or decay?)
f(t) = 1600(1.03)t; 2,150 people
f(t) = 1600(0.97)t; 1,738 people
f(t) = 1600(1.03)t; 2,128 people
f(t) = 1600(0.97)t; 1,819 people
Kimi invests $4,000 at 3% interest compounded continuously. How much money will she have in 4 years?
(a)
Dash invested $10,000 at 3% interest compounded continuously. How much will he have after 8 years?
(a)
Damara invests $3500 at 2% compounded continuously for 5 years. How much will she have in her account after 5 years?
(a)
Interest Rate: 3.75%
Time: 25 years
Compounded Monthly
State the future account balance.
Willie invests $8,515 in a retirement account with a fixed annual interest rate of 5% compounded continuously. What will the account balance be after 20 years?
$22,017.32
$23,146.17
$20,021.95
$20,943.52
Jessica invests $3,948 in a savings account with a fixed annual interest rate of 9% compounded continuously. What will the account balance be after 11 years?
$8,786.44
$10,056.40
$10,624.99
$8,357.92
Adam invests $5,208 in a savings account with a fixed annual interest rate of 8% compounded continuously. What will the account balance be after 8 years?
$9,876.87
$10,699.49
$9,489.59
$8,803.91
What does the P stand for in this formula?
Initial amount
Final amount
Rate
Time
The number of times compounded per year.
What does the r stand for in this formula?
Rate as a percent
Rate as a decimal
number of times interest is compounded
What does the t stand for in this formula?
time in weeks
time in months
time in years
the number of times interest is compounded per year
Jessica invests $3,948 in a savings account with a
fixed annual interest rate of 9% compounded continuously. What will the account balance be after 11 years?
$8,786.44
$10,056.40
$10,624.99
$8,357.92
Sumalee invests $6,227 in a savings account with a
fixed annual interest rate of 8% compounded continuously. What will the account balance be after 6 years?
$10,685.57
$11,011.00
$10,369.77
$10,063.30
Chelsea invests $2,709 in a savings account with a
fixed annual interest rate of 8% compounded continuously. What will the account balance be after 6 years?
(a)
The formula below can be used to determine the total amount of money in a savings account. What was the initial amount of money deposited in the account?
A=3250e0.062⋅8
(a)
The formula below can be used to determine the total amount of money in a savings account. What is the interest rate as a percent?
A=3250e0.062⋅8
(a)
The formula below can be used to determine the total amount of money in a savings account. How long was the money left in the account?
A=3250e0.062⋅8
(a)
The formula below can be used to determine the total amount of money in a savings account. How much money will end up being in the account if no other deposits or withdrawals are made?
A=3250e0.062⋅8
(a)
