The average annual cost of tuition...

Question

The average annual cost of tuition, room, and board for public colleges and universities has been growing exponentially by 6.17% each year since the year 1981. The average cost of tuition, room, and board in 1981 was $2665.32. Part A : Write an exponential function that can be used to model the average cost of tuition, room , and board as a function the number of years past 1981.

Part B: If this trend continues, when will the average cost of tuition, room, and board exceed $35,000? Explain or show your thinking.

Answer 1

C(t) = 2665.32(1.0617)^t

35000 = 2665.32(1.0617)^t

13.1316 ≈ (1.0617)^t

ln 13.1316 ≈ ln 1.0617 t

2.5750 ≈ 0.0599 t

43.00 ≈ t