Question

An online store started its business with 15 sales per week. If their sales increased 18% each week, use an exponential model to find the week in which they exceeded 1000 sales per week. Remember, A= P(1+r)^t26 weeks31 weeks38 weeks15 weeks

Answer 1

Given,

The initial sale is 15.

The rate of increase of sale per week is 18 %.

The final sale is 1000.

The week at which the sales exceeds 1000 is:

`\begin{gathered} 1000=15*(1+(18)/(100))^t \\ (1000)/(15)=((118)/(100))^t \\ (200)/(3)=(1.18)^t \\ log\text{ \lparen}(200)/(3))=t\text{ log\lparen1.18\rparen} \\ t=25.37 \end{gathered}`

The sales of the business reach to 1000 in 25th week.

Hence, the sales of the business exceed to 1000 in 26th week.