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?
1 The resale value of a car drops by a fixed percentage each year. A particular kind of car sells for $32,000, and its value drops by 12.5% each year a. When the car is brand-new (x=0), how much is it worth? $32,000 b. How much is it worth after 1 year (x=1)? c. After two years (x=2)? After three years (x=3)? Four (x=4)? d. What is the form of this function (linear, quadratic, or exponential)? e. If it’s exponential, what is the initial value? The base? Is it growth or decay? |
2 Sally is selling lemonade, for $1.25 a glass. She starts with $20 in cash, and hopes that by selling lemonade she will finally be able to get the power drill she’s been wanting. a. When Sally starts the day (x=0), how many dollars does she have? $0 b. How many dollars will she have after the first sale (x=1)? c. After the sale (x=2)? The third (x=3)? The fourth (x=4)? d. What is the form of this function (linear, quadratic, or exponential)? e. If it’s exponential, what is the initial value? The base? Is it growth or decay? |
3 Mrs. Bidwell’s club rules are that every student should high-five every other student. She starts out her year with only two students, but a new one joins the club every day. a. How many high-fives happen at the start (x=0), with 2 students? 1 b. How many high-fives happen the next day (x=1), with 3 students? c. With a fourth? (x=2)? A fifth (x=3)? A sixth (x=4)? d. What is the form of this function (linear, quadratic, or exponential)? e. If it’s exponential, what is the initial value? The base? Is it growth or decay? |
4 A meme goes viral on the internet, starting with one person posting an animation of a puppy doing a backflip into a pile of laundry. Every person that sees the meme falls in love with it, sharing it with 25 new friends. a. When the person posts it (x=0), how many total times has it been shared? 1 b. How many times will it have been shared after those friends share it (x=1)? c. When x=2? When x=3? When x=4? d. What is the form of this function (linear, quadratic, or exponential)? e. If it’s exponential, what is the initial value? The base? Is it 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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