Question

An air-freshener starts with 21 grams and evaporates over time. In each of the following cases, enter a formula for the quantity, Q grams, of air-freshener remaining t days after the start.

a. The decrease is 7 grams a day.
b. The decrease is 6% per day.
c. The decrease is at a continuous rate of 10% per day.

Answer 1

a.) Q= 21 - 7t

b.) Q = 21 - 1.26t

c.) Q = 21 - 2.1t

Explanation:

a.) if it starts with 21grams, and it decreases with 7grams per day, then the remainder after t days becomes:

Q= 21 -7t.

For example, after one day, that is when t=1, the remainder becomes

Q= 21 - 7(1) = 14grams.

b.) if the decrease is 6% per day, we first calculate the 6% of 21, that is

21 * 6/100 = 1.26.

Hence, after t days, the remainder becomes:

Q= 21 - 1.26t.

For example, after 3 days, that is when t=3, the remainder becomes:

Q= 21 - 1.26(3) = 21 - 3.78

Q= 17.22grams.

c.) if the decrease is at 10% per day, and 10% of 21grams is 2.1grams, then the remainder becomes:

Q= 21 - 2.1t