1. [7 marks] Mia runs a medium-size business whose profit is in thousands of dollars at a certain time t in months can be modeled by the function P(t) = B (1 e^(rt)). Suppose B = 100 and r = 1/80 .

(b) Express the variable t as a function of P by hand and compare with your answer from (a) above. Explain the meaning of the function t.

(c) Using the function t of P in (b), how long does it take Mia to get a $50, 000 profit? Round off your results to two decimal places.

(d) What is the maximum possible profit Mia can make using P(t)? [Hint: Use the function t of P in (b) above.]