Exponential Functions Word Problems
Properties of Exponential Functions
Growth or Decay?
Functions (from a table)
Functions (from a scenario)
Miscellaneous
100
A rumor is spreading and originally only 3 people knew the rumor. Every day, the number of people who knows doubles.
How many people will know in a week?
384 people
100
Consider the exponential function: f(x) = 3(12)x
What is the constant ratio?
b =12.
100
A function has a constant ratio(b-value) of 3.
Is this growth or decay?
growth - because 3 is greater than 1.
100
What's the y-intercept?
y-intercept: (0,5)
100
In 2010, your favorite snack cost $4. With inflation, the price is increasing by % 2each year.
Write a function to represent this scenario.
f(x) = 4(1+0.02)x or f(x) = 4(1.02)x
100
A function is increasing by 45%. What is the constant ratio (b-value)?
b = 1 + 0.45
b = 1.45
200
You are bidding on an item at an auction. At 3pm, the price was $50. It seems to be increasing its price by 25% every hour.
How much will it be bidding for by 8pm?
$152.59
200
Consider the exponential function: f(x) = 10(0.5)x
What is the y-intercept?
The y-intercept is (0, 10)
200
A function has a constant ratio(b-value) of 0.3.
Is this growth or decay?
Decay - because 0.3 is less than 1.
200
What's the constant ratio?
b =2
200
Write an exponential function for this scenario.
f(x) = 12,000(1+0.06)x
or f(x) = 12,000(1.06)x
200
A function is decreasing by 20%. What is the constant ratio (b-value)?
b = 1 - 0.2
b = 0.8
300
The deer population has doubled every year since 2020. The current population of deer is 51,584. What was the population of deer in 2020?
3224
300
What is the difference between a linear function and an exponential function?
Linear functions have constant change (adding the same amount).
Exponential functions don't have constant change, but they do have a constant ratio (multiplier).
300
f(x)=25(1.07)x
Does this function represent exponential growth or decay?
Exponential Growth.
300
Write the exponential function represented by this table. (Round the constant ratio)
f(x) = 5,005(1.2)x
300
Write the function AND answer the question.
Function: f(x) = 18,000(1 - 0.02)x
or f(x) = 18,000(0.98)x
After 3 years the population will be: 16,941 people
300
A function is increasing by 2%. What is the constant ratio (b-value)?
b = 1 + 0.02
b = 1.02
400
Antibiotics work to kill bacteria inside your body. It decreases the bacterial load by 10% every hour. If your initial viral load was 5,000, how many full hours will it take for your viral load to be under 500?
22 hours
or ~21.85 hours
400
Decay functions have a constant ratio that is between _____ and ____
It is between 0 and 1
400
f(x)=1300(0.98)x
Does this function represent exponential growth or decay?
Exponential Decay
400
Write the exponential function represented by this table.
f(x) = 2100(1.03)x
400
You put $500.00 into an account and the account earns 4% interest, compounded annually (each year). How much will be in the account after 5 years?
Write the function AND answer the question.
Function: f(x) = 500(1 + 0.04)x
or f(x) = 500(1.04)x
After 5 years, the account will have: $608.33
400
A zombie outbreak is modeled by the function where x measures the number of days:
f(x) = 4(1.15)x.
1) How many zombies started the outbreak?
2) How many zombies will there after a week (7 days)?
1) 4 zombies started the outbreak
2) There will be 10 zombies after 7 days.
500
The population of fox decrease as the bunny population also decreases. The fox are decreasing by 35% each year. If the population started at 8000 this year, approximately how many fox will exist in 2027?
2197 fox
500
Growth functions have a b value that is ______ than 0
greater
500
f(x)=25(1)x
Does this function represent exponential growth or decay?
Neither!
500
Write the exponential function represented by this table.
f(x) = 20(0.5)x
500
Your car cost $42,500 when you purchased it in 2015. The value of the car decreases by 15% annually (each year)
What is the value of your car now?
f(x) = 42,500(1 - 0.15)x or
f(x) = 42,500(0.85)x
Your car's value now (8 years later) is: $11,580.85
500
2243