Question

An air freshener starts with 33 grams and evaporates. In each of the following situations define a function that gives the remaining mass of the air freshener (in grams) in terms of the number of days, t t, since the air freshener was first used.

Answer 1

Hello!

A) The mass of the air freshener A decreases by 3.2 grams each day. Define a function, f, to represent this situation.

In this function, the mass of the air freshener A (m) is the dependent variable and the days (t) and the initial amount of the air freshener A (mi) are the independent variables. If the mass decreases by a fixed amount each day, you only have to multiply this amount by the number of days:

$m=mi-(3,2*t)$

B) The mass of the air freshener B decreases by 3.2% each day. Define a function, g, to represent this situation.

This function is trickier since there isn't a fixed amount of decreasing. Instead, the rate of decreasing depends on the initial amount of the freshener (mi). You have to include this initial amount in the equation to correctly model it. This is how you do it:

$m=mi-(mi* \frac{3,2}{100}*t)$

Have a nice day!