An air freshener starts with 25 grams and evaporates. In each of the following cases, write a formula for the quantity, Q grams, of air freshener remaining t days after the start.

(a) The decrease is 4 grams per day.

(b) The decrease is 9% per day.

(c) The decrease is at a continuous rate of 12% per day.

Question

Mathematics

Esther

29 December, 11:06

An air freshener starts with 25 grams and evaporates. In each of the following cases, write a formula for the quantity, Q grams, of air freshener remaining t days after the start.

(a) The decrease is 4 grams per day.

(b) The decrease is 9% per day.

(c) The decrease is at a continuous rate of 12% per day.

+4

Answers (1)

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Dominic York · Answer 1

A) Decrease is a constant rate. Therefore the function will be linear.

Q = 25 - 4t

b) Decrease is exponential. You will have a exponential function.

Q = 25 (1-.09) ^t = 25 (.91) ^t

c) Decrease is exponential. You will have a continuous exponential function.

Q = 25e^ (-.12t)