Question

Suppose that the sales at Borders bookstores went from 7878 million dollars in 19921992 to 412412 million dollars in 19971997. Find an exponential function to model the sales (in millions of dollars) as a function of years, tt, since 19921992.

Answer 1

S(t) = 78000000*e^0.333t

Explanation:

Given the following :

Sales in 1992 = $78 million

Sales in 1997 = $412 million

Exponential function that models the sales in millions of dollars as a function of years t since 1992.

S(t) = So*e^kt

S(t) = sales in t years ; So = Initial or starting sales

Find k :

S(t) = sales in 1997 = $412,000,000

So = sales in 1992 = $78,000,000

t = 1997 - 1992 = 5

412,000,000 = 78,000,000 × e^k5

412,000,000 = 78,000,000 × e^5k

412,000,000/ 78,000,000 = e^5k

5.2820512 = e^5k

In(5.2820512) = In(e^5k)

1.6643145 = 5k

k = 1.6643145 / 5

k = 0.3328629

k = 0.333 ( to 3 decimal places)

Hence,

S(t) = 78000000*e^0.333t