51 Exponential Functions and Their Graphs 369 59 Inflation A

5.1 Exponential Functions and Their Graphs 369 59. Inflation Assuming that the annual rate of inflation averages 4% over the next 10 years, the approximate costs C of goods or services during any year in that decade can be modeled by C(t) = P(1.04), where t is the time in years and P is the present cost. The price of an oil change for your car is presently $29.88. Estimate the price 10 years from now

Solution

C = P(1.04)^t

Now, here t is in DECADES
cuz it says 4% inflation(as in it becomes 104% or 1.04 times)
in 10 years(1 decade)

So, t is in decades

Now it is .29.88

So,
C = 29.88 * (1.04)^t

10 yrs from now, or 1 decade from now,
therefore, plug in t = 1 :

29.88(1.04)^1

29.88*1.04

31.0752 dollars ----> ANS