Rusty wants to compare two different air fresheners Air Clea

Rusty wants to compare two different air fresheners. Air Clean sells an air freshener that initially weighs 32 grams and evaporates such that the mass of the air freshener decreases by 2.5% each day. Fresh Air sells an air freshener that initially weighs 28 grams and evaporates such that the mass of the air freshener decreases by 1.8% each day.

Suppose Rusty opens both air fresheners at the same time. After how many days will the two air fresheners weigh the same? Round your answer to the nearest day.

Solution

First sample decreases according to: A1(t) = 32*exp(-t*0.025)

the second one:                              A2(t) = 28*exp(-t*0.018)

the day they they\'ll weigh equally is found from:

A1(t)=A2(t)

32*exp(-t*0.025)=28*exp(-t*0.018)

32/28=exp(t*0.007)

and, finally,

-t=ln(32/28)/0.007 = 19.1 (days)=19 days