Question

Suppose a company's revenue increased by 12.3% over the previous year. assuming this trend continues, which expression could the company use to approximate the percent increase in revenue through a certain number of months, m?

Answer 1

The required expression would be
`(1.0097)^m`

Step-by-step explanation:

Let
`R_0` be the initial revenue,

Since, the company's revenue increased by 12.3% over the previous year,

So, the company's revenue after m months

`R = R_0 ( 1 +(12.3)/(100))^(m)/(12)`

(∵ 1 year = 12 months)

⇒
`R = R_0 ( 1 +0.123)^(m)/(12)`

⇒
`R = R_0 ( 1.123)^(m)/(12)`

⇒
`R = R_0 ((1.123)^(1)/(12))^m` ( using power of power property of exponent )

⇒
`R = R_0 (1.0097)^m`

Hence, the required expression would be
`(1.0097)^m`