Question

Sales of a certain product are declining at a rate proportional to the amount of sales. If at the end of the first year the sales have declined by 20%, then how many years will have passed (since the beginning of the first year) when sales become only 27% of their original value

Answer 1

Answer:

6.5 years

Step-by-step explanation:

Given that:

Product sales declines at a rate proportional to the amount of sales

Decline at the end of first year = 20%

Let :

sales = y

Hence ;

y = e^-0.2t (exponential decline rate of 20% = 0.2)

t = time in years

Time that would have passed when sales become 27% of original value ;

y = 27% = 0.27

y = e^-0.2t

0.27 = e^-0.2t

Take the In of both sides

In 0.27 = - 0.2t

−1.309333 = - 0.2t

−1.309333 / - 0.2 = t

t = 1.309333/0.2

t = 6.5466665

t = 6.5 years