Question

In a certain area the consumption of electricity has increased at a continuous rate of 8%. If it continued to increase at this rate, find the number of years before three times as much electricity would be needed

Answer 1

It will take 14.3 years

Explanation:

Let the consumption of electricity presently be X kw/h

In the next three years, we would be expecting an increase to 3x kw/h

Since we do not know the number of years it will take, let us represent this by t years.

We can represent the consumption in the next three years by the equation;

x × (1 + 8%)^t = 3x

(1+0.08)^t = 3

(1.08)^t = 3

We can use natural logarithms to get what t is

take the natural logarithm of both sides

ln(1.08)^t = ln3

tln1.08 = ln3

t = ln3/ln1.08 = 1.0986/0.077

t = 14.3 years