Graphs
Growth or Decay
Geometric
Percent Rate
Word Problems
100
Does the graph show exponential growth or decay?
Exponential Growth
100
How do I know if the exponential relationship below is growth or decay?
y = 3(0.56)x
Decay has a b value or decay factor less than 1.
decay factor = (1 - rate as a decimal)
1 - 0.56 = 0.44
Subtract 0.44 from 1 to get 0.56
100
What is the equation for the nth term of a geometric sequence?
a_n=a_1*r^(n-1)
100
Is this exponential growth or decay?
What is the rate of growth/decay as a percent or a decimal?
y=5(0.2)^x
Exponential Decay - the factor is less than 1.
Decay rate = 80% or 0.8
How did you get the factor of 0.2?
1 - 0.8 = 0.2
100
y=2300(0.995)^t
The exponential function above models the enrollment in a high school, where t is the number of years after 2019. How many students will be enrolled in 2025?
2,232 students
200
The graph represents the fish population after t years.
What was the fish population when it was first measured?
1,000 fish
(the y-intercept value, when x = 0))
200
Do the following equations represent exponential growth, decay, or neither?
y=5x+6
Neither (It's linear! y=mx+b)
200
Arithmetic, geometric, or neither.
-6, 12, -24, 48...
Geometric
200
Is this exponential growth or decay?
What is the percent growth/decay rate?
y=5(1.3)^x
Exponential Growth
30%
200
The cost of in-state tuition at UWSP in 2020 was $8,404 per year. If the cost is increasing at a rate of 2% per year, what will the cost of tuition be in 2024?
Round to the nearest dollar.
$9,097 per year
y=8404(1+0.02)^4
300
Does the graph show exponential growth or decay?
What is the growth/decay factor?
Exponential Decay
Decay factor = 0.25
4 -: 16 = 0.25
300
y=2(1.13)x
Does this function represent exponential growth or decay? What is the growth/decay factor?
Exponential Growth
Factor: 1.13
300
Write the equation for the nth term:
768, 192, 48, 12, 3, ...
a_n=768*(1/4)^(n-1)
300
Is this exponential growth or decay?
What is the percent growth/decay rate?
y=1(0.01)^x
Exponential Decay
99%
300
The population of Madison, WI was 215,000 in 2000 and grew by 1.1% each year until 2024. What was the population in 2024?
Round to the nearest person.
266,552 people
y=215,000(1+0.011)^24
400
The value of the boat is decreasing by 10% each year since it was purchased. What was the purchase price?
$8,000
400
y=5(0.97)x
Does this function represent exponential growth or decay? What is the rate of growth or decay?
Exponential Decay
Rate: 0.03 or 3%
400
What is the 8th term of a sequence with
a_1=6
r = 2
768
400
Is this exponential growth or decay?
What is the percent growth/decay rate?
y=1/2(0.7)^x
Exponential Decay
30%
400
Is the function exponential growth or decay?
What is the factor of growth/decay?
Exponential Decay
Decay factor: 0.9
500
How can you tell if a geometric sequence will not follow an exponential curve?
If r is negative.
500
Mrs. Linear purchased a car for 26,400 and every year it depreciates in value by 12%. What can she expect the value of her car to be after 3.5 years?
y=26400(0.88)3.5=$16,876.92
500
Write an equation for the nth term of the geometric sequence:
4/5, 4, 20, ...
a_n=(4/5)(5)^(n-1)
500
Is this exponential growth or decay?
What is the percent growth/decay rate?
y=1/2(1.07)^x
Exponential GROWTH
7%
500
If you put $500.00 into an account and the account earns a 3% yearly interest rate. How much will be in the account after 5 years?
Round the nearest cent!
$579.64