Create a Function
Growth or Decay
Interpret
Graphs+Tables
Growth/Decay Rate
200
If a=2 and b=3, What is the equation of the exponential function?
y=2(3)x
200
Does this function represent exponential growth or decay? Explain.
Exponential growth, the graph is increasing
200
The population of Sanibel, Florida can be modeled by P = 6191 · 1.05t, where t is the number of years since 2016. What was the population in 2016? What percent did the population increase by each year?
Population in 2016 = 6191
Population increased by 5% each year
200
Fina a and b.
a=2, b=3
200
What is the growth rate for the function y=5(1.2)x?
20%
400
If the y-intercept is 10 and the common ratio is dividing by 2, what is the equation of the exponential function?
y=10(1/2)x
400
Your car cost $42,500 when you purchased it in 2017. The value of the car depreciates by 15% annually. Does this represent exponential growth or exponential decay? Explain.
Exponential decay, "depreciates"
400
Sarah is depositing some money in a savings account and her account balance can be modeled with the function f(x)=200(1.02)x What does the 200 represent? What does the .02 represent?
She initially had $200 in her account.
0.02=2% interest rate on her savings account
400
a=10, b=1/2
400
Does this function have a growth or decay rate? What is it?
f(x)=0.4(0.13)x
Decay, 87%
600
A newly hatched channel catfish typically weighs about 0.06 grams. During the first 6 weeks of life, its weight increases by about 10% each day. Write a function to model the situation.
y=0.06(1.10)x
600
Fred’s bank account balance started with $325, he has an annual interest rate of 4%. Does this represent exponential growth or exponential decay? Explain.
Exponential growth, they are gaining the interest
600
A certain strain of bacteria triples every hour. What does f(5)=243 mean in context?
After 5 hours there are 243 bacteria
600
Write the exponential function for the table.
y=32(1/2)^x
600
The function f(x) = 350(0.25)x models the amount of money remaining in Alicia’s summer budget, where x represents the number of weeks since summer began. What is the growth/decay rate?
Decay, 75%
800
You bought $2,000 worth of MathNation stocks in 2014. The value of the stocks decreases by 4% each year. Write an exponential function to represent this situation.
y=2000(0.96)x
800
y = 5575 · (0.65)t
Does this function represent exponential growth or exponential decay? Explain.
Exponential decay, b=0.65 < 1
800
To grow a business, its members have to recruit new members every month. Its growth can be modeled by y=10(2)x How many members were there originally? What is an appropriate domain? (Specify what type of numbers)
There were originally 10 members
Domain = (months) x is rational
x >= 0
800
y=2(3)x
800
A snake is 100 mm long. It increases in length by 12% every week. What is the b value?
b=1.12
1000
Landon bought a new car for $16,000. After 1 year, the car is worth $15,200. Write a function that describes the value, C(t), of the car after t years.
y=16000(0.95)x
1000
y = 100(1.25)t
Does this function represent exponential growth or exponential decay? Explain.
Exponential growth, b=1.25>1
1000
An adult takes 400 mg of vitamin c. Each hour, the amount of vitamin c in the person’s system decreases by about 29%. Find f(2). What does it represent?
f(2)=201.64
After 2 hours, the amount of vitamin c in the person's system is 201.64 mg.
1000
Find f(10) and explain what it represents.
10 years before 2020 (2010), the average US movie ticket price was around $8
1000
Marisa deposits $250 into a bank account that she has to pay a 1.4% fee annually. What is the b value?
b=0.986