Exponentialgrowth occurs when a quantity increases by the same factor over equal intervals of time.
Exponentialdecay occurs when a quantity decreases by the same factor over equal intervals of time.
For exponential growth, the value inside the parentheses is greater than 1 because r is added to 1.
For exponential decay, the value inside the parentheses is less than 1 because r is subtracted from 1.
Let's practice finding the growth/decay factors:
Question 1
1.
A bank will pay you a 3% per year interest on your account.
What is the growth/decay factor?
Question 2
2.
A car depreciates in value 8% per year.
What is the growth/decay factor?
Question 3
3.
The value of the house increases by 15% per year.
What is the growth/decay factor?
Question 4
4.
Donovan's investment lost 4.5% interest last year.
What is the growth/decay factor?
Question 5
5.
Minh's saving account earned him 0.25% interest last month.
What is the growth/decay factor?
Question 6
6.
Emma's salary will increase by 1.75% each year.
What is the growth/decay factor?
Question 7
7.
Joe's charity organization has seen a loss of 12.25% over the last year.
What is the growth/decay factor?
Question 8
8.
Florida's alligator population has decreased by 2.5% the last 5 years.
What is the growth/decay factor?
Question 9
9.
The sales of laptops has increased by 37.5% this year.
What is the growth/decay factor?
Question 10
10.
Taxes have increased by 6.375% .
What is the growth/decay factor?
Let's complete some examples together.
Question 11
11.
The population of a city is 50,000 and is growing 3% each year. Determine the population of the city after 5 years. Round your answer to the nearest whole number.
Question 12
12.
A $6000 investment has a 7% loss each year. Determine the value of the investment after 3 years. Round your answer to the nearest cent.
Question 13
13.
The cells in a science experiment double every hour. How many cells would there be if the experiment began with 15 cells after 6 hours?
Now, complete the remaining problems for homework. Show your work in the space provided.
Question 14
14.
The starting salary for a new employee is $25,000. The salary for this employee increases 4% annually. Determine the employee’s salary after 15 years. Round your answer to the nearest cent.
Question 15
15.
The population of a city is 3,000,000 and is decreasing by 2% each year. Determine the population after 10 years. Round your answer to the nearest whole number.
Question 16
16.
You put $250 in a savings account that earns 2% annual interest compounded yearly. You do not make any deposits or withdrawals. How much will your investment be worth in 6 years? Round your answer to the nearest cent.
Question 17
17.
In 2017, a person purchased a car for $25,000. The value of the car decreased by 14% annually. Determine the value of car in 2021 when they traded it in. Round your answer to the nearest cent.
Question 18
18.
In a scientific study, the number of insects triples every 2 months. The study began with a sample of 30 insects. Determine the number of insects after 1 year.
Question 19
19.
An investment doubles every 8 years. What is the value of a $500 investment after 40 years?
Question 20
20.
During an economic recession, a charitable organization found that its donations dropped by 1.1% per year. Before the recession, its donations were $390,000. Estimate the amount of the donations 5 years after the start of the recession. Round your answer to the nearest cent.
Question 21
21.
Suppose the acreage of forest if decreasing by 2% per year because of development. If there are currently 4,500,000 acres of forest, determine the amount of forest land after 7 years. Round your answer to the nearest whole number.
Question 22
22.
Suppose one of your ancestors invested $500 in 2006 in an account paying 4% interest compounded annually. Find the account balance after 2021. Round your answer to the nearest cent.
Question 23
23.
Suppose you invest $1500 in an account paying 4.75% interest. Find the account balance after 25 years with the interest compounded annually. Round your answer to the nearest cent.
Question 24
24.
A $10,500 investment has a 15% loss each year. Find the value of the investment after 4 years. Round your answer to the nearest cent.
Question 25
25.
A city of 140,000 people has a 1% annual decrease in population. Determine the city's population after 10 years. Round your answer to the nearest whole number.
Question 26
26.
The starting salary for a new employee is $25,000. The salary for this employee increases by 8% per year. What is the salary after 3 years?Round your answer to the nearest cent.
Question 27
27.
An investment of $750 is placed in an account paying 5.25% interest compounded annually. Find the account balance after 7 years. Round your answer to the nearest cent.
Question 28
28.
Suppose a new car is worth $21,000. Its value decreases by 18% each year. Find the value of the car after 5 years. Round your answer to the nearest cent.
Question 29
29.
A $25,000 purchase has a 12% decrease in value per year. Determine the value of the purchase after 9 years. Round your answer to the nearest cent.
Question 30
30.
An investment of $400 doubles in value every 5 years. Determine the value of the investment after 20 years.
Question 31
31.
Please upload pictures of your work if you didn't use the space provided.
Question 32
32.
Please upload pictures of your work if you didn't use the space provided.
Question 33
33.
Please upload pictures of your work if you didn't use the space provided.
Question 34
34.
Please upload pictures of your work if you didn't use the space provided.
Question 35
35.
Please upload pictures of your work if you didn't use the space provided.
