Word Problems
A new car that sells for $18,000 depreciates 25% each year. Write a function that models the value of the car. Find the value of the car after 4 yr.
f(x)= 18,000(.75)^x
f(4)= $5695.31
150(0.8)^12
10.30792
What is the a value?
The initial value (or starting amount) of the function when x=0.
f(x)=3^x
What happens to the graph if it translates up 3 units?
g(x)=3^x+3
A baseball card bought for $50 increases 3% in value each year. Write an exponential function that represents this model.
f(x)= 50(1.03)^x
90(1.68)^6
2023.4767
What does exponential growth mean?
A process where a quantity increases at a rate proportional to its current size, resulting in faster growth as it gets larger
f(x)=8^x
What happens if the graph translates down 8 units?
g(x)=8^x-8
The population of an endangered bird is decreasing at a rate of 0.75% per year. There are currently about 200,000 of these birds. Write a function that models the bird population.
f(x)= 200,000(.999925)^x
17(.52)^3
2.3903
What is the b value?
The constant multiplier, growth factor, or decay factor.
f(x)=(0.95)^x
What happens if if the graph has a vertical stretch by a factor of 2?
g(x)=0.95^x(2)
A computer valued at $6500 depreciates at the rate of 14.3% per year. Write a function that models the value of the computer. Find the value of the computer after three years.
f(x)= 80(.965)^x
f(3)= 47 years
121(.71)^6
15.5001
What does exponential decay mean?
A process where a quantity decreases by a consistent percentage over regular time intervals, rather than by a fixed amount
f(x)=(0.5)^x
What happens to the graph if there is a vertical compression by a factor of 1/4 and reflection over the x axis?
g(x)=0.95^x(1/4)