Question

Demand for electrical services in your area is $12 million per year. It is expected to grow 10% compounded annually

over the next 5 years. What will demand be in 5 years? The formula for compound growth is E-Bx (1 + R)', where E is ending value, B is
beginning value, R is rate of growth, and T is the amount of time.

Answer 1

`\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &\stackrel{millions}{\$12E6}\\ r=rate\to 10\%\to (10)/(100)\dotfill &0.10\\ t=\textit{elapsed time}\dotfill &5\\ \end{cases} \\\\\\ A=12E6(1 + 0.10)^(5)\implies A=12E6(1.1)^5\implies A=19326120`

Answer 2

$19.3 million

Explanation:

The demand in 5 years can be found by using the given formula for exponential growth with the given beginning value, growth rate, and time.

E = B(1 +r)^t

You are given B = 12, r = 0.10, t = 5, so the ending value is ...

E = 12(1 +0.10)^5 = 12(1.61051) = 19.32612

Demand for electrical services in 5 years will be about $19.3 million per year.