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

If the company's trend increases by 12.3% over the previous year and this is bound to continue then the percentage increase through a given number of months will be given by:
   (1+ 0.123)∧m/12
 we get (1.123)∧m/12
Simplifying the expression we get (1.123)∧(1/12)m
Evaluating (1.123)∧(1/12) we get 1.00971
Therefore, the expression to represent monthly percentage increase will be 
   (1.00971)∧m

Answer 2

Answer:

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

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

$R = R_0 ( 1 +\frac{12.3}{100})^\frac{m}{12}$

(∵ 1 year = 12 months)

⇒ $R = R_0 ( 1 +0.123)^\frac{m}{12}$

⇒ $R = R_0 ( 1.123)^\frac{m}{12}$

⇒ $R = R_0 ((1.123)^\frac{1}{12})^m$  ( using power of power property of exponent )

⇒ $R = R_0 (1.0097)^m$

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