SOLUTION: Suppose the price of a first-class stamp was 4¢ for the first time in 1958 and 44¢ in 2009. Find a simple exponential function of the form y = ab^t that models the cost of a fi

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Suppose the price of a first-class stamp was 4¢ for the first time in 1958 and 44¢ in 2009. Find a simple exponential function of the form y = ab^t that models the cost of a fi      Log On


   

Question 1148044: Suppose the price of a first-class stamp was 4¢ for the first time in 1958 and 44¢ in 2009. Find a simple exponential function of the form
y = ab^t that models the cost of a first-class stamp for 1958 - 2009. (Let
t = 0 correspond to 1958. Assume y is in dollars. Round your value for b to four decimal places.)
y=???
Also how would i predict tha value for 2020?
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Year 1958 is t=0; so year 2009 is t=51.

The price in 1958 (t=0) was .04 dollars (4 cents):
ab%5E0+=+0.04
a%281%29+=+0.04
a+=+0.04

The price in 2009 (t=51) was .44 dollars (44 cents):
0.04%2Ab%5E51+=+0.44
b%5E51+=+0.44%2F0.04+=+11
b+=+11%5E%281%2F51%29

The rest I leave to you....

(1) Use a calculator to evaluate b
(2) Form your equation y = ab^t
(3) Check your answer by verifying that ab^51 to the nearest cent is 44 cents
(4) For year 2020 (t=62), evaluate ab^62