Maths Question on Exponential Functions?

Question

The proportion of people responding to a TV advertisement of a new product after it has been on the market for t days is given by :

P = 1 - e^-0.2t

The marketing area contains 10,000,000 potential customers and each response to the advertisement yields a gross profit of 70 cents (gross profit = sales - cost of good sold). The advertisement costs $30,000 to produce and $5000 for each day it runs.

A) Find the value of P when t is very large and interpret its meaning.

B)Find an expression for advertising costs over time and hence obtain an expression for net profits over time. (net profit = gross profit - advertising expenses)

Answer 1

A) when t is very large e^-.2t goes to 0 so that means 100% of the people have responded.

B)  You know advertising expenses = 30,000 + 5,000t  

gross profit = (1-e^-.2t)(10,000,000)(0.70)