Decide whether each situation is best described by a linear, quadratic, or exponential function.
If the function is exponential: What is the growth factor. Is it doubling (factor of 2)? Tripling (factor of 3)? Factor of 5? 10?
Car Values
A particular kind of car sells for $32,000, and its resale value drops by 12.5% each year.
1 Is the function increasing or decreasing?
2 When the car is brand-new (x=0), how much is it worth?
3 How much is it worth after…
| (1 year) x=1 |
(2 years) x=2 |
x=3 | x =4 |
|---|---|---|---|
|
4 What is the form of this function? linear ☐ quadratic ☐ exponential☐
5 If it’s exponential,
Fill in the coefficients to write a function that shows the value of the car after a given number of years:
f(x) = initial value a growth factor b x + horizontal asymptote k
Is it exponential growth? ☐ or decay? ☐
Lemonade Stand
Sally is selling lemonade, for $1.25 a glass in hopes of finally be able to get the power drill she’s been wanting. She starts with $20 cash.
6 Is the function increasing or decreasing?
7 When Sally starts the day (x=0), how many dollars does she have?
8 How many dollars will she have after…
| (first sale) x=1 |
(second sale) x=2 |
x =3 | x = 4 |
|---|---|---|---|
|
9 What is the form of this function? ☐ linear ☐quadratic ☐ exponential
10 If it’s exponential,
Fill in the coefficients to write a function that shows how much Sally has saved after a given number of sales:
f(x) = initial value a growth factor b x + horizontal asymptote k
Is it exponential growth? ☐ or decay? ☐
These materials were developed partly through support of the National Science Foundation, (awards 1042210, 1535276, 1648684, 1738598, 2031479, and 1501927). 
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