Question: Since 1980, textbook prices have increased at 6.7% per year while inflation has been 3.3% per year.7 Assume both rates are continuous growth rates and let time, t, be in years since the start of 1980.
(a) Write a differential equation satisfied by B(t), the price of a textbook at time t.
(b) Write a differential equation satisfied by P(t), the price at time t of an item growing at the inflation rate.
(c) Solve both differential equations.
(d) What is the doubling time of the price of a textbook?
(e) What is the doubling time of the price of an item growing according to the inflation rate?
(f) How is the ratio of the doubling times related to the ratio of the growth rates? Justify your answer.