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 fresheners 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

The Air Clean exponentially decays as follows: a(t)= 32*exp(-0.025t) , where \'t\' is in days and a(t) in grams.

The Fresh air exponentially deacys as follows: b(t)= 28*exp(-0.018t)

For finding the days after which they will weigh the same: a(t)=b(t)

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

(32/28) = exp(0.007t)

Taking logarithm, we get: t= ln(32/28)/0.007 = 19 days (Answer to the nearest integer)