Answer:
S(t) = 78000000*e^0.333t
Step-by-step 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
