AP Calculus AB
Example: Suppose the same business owner in the previous example decided to close down his business and
start a new business. He has just come across some great news from one of his old time friends that this next
business he should go into is fail proof. The friend tells him he can never lose his investment money. This
sounds all too enticing for him to say no and so he jumps right in and starts planning for his future because all
he has left in the bank is $ 406.
What he doesn’t know is that the business model he just jumped right into is modeled after the equation,
𝑃(𝑡) = 406 + 𝑡𝑒 −.25𝑡 where P(t) is his net profit and t is time in months. In his excitement, he takes on
additional loans to purchase new equipment to grow his business.
a) At what time t in months will he reach his maximum profit.
b) As his current friend, do you advise him to continue or do you advise him to stop?