Question

The consumption rate of​ electricity, in​ kW/h has​ increased, on​ average, at 3.5​% per year. If it continues to increase at this rate​ indefinitely, find the number of years before the electric companies will need to double their generating capacity.

The electric utities will need to double their generating capacity in about _____ years.

Answer 1

20.14

Explanation:

Given that the consumption rate of​ electricity, in​ kW/h has​ increased, on​ average, at 3.5​% per year.

So if initial consumption is C after one year it would be

`(1+0.035)C` and after 2 years
`(1+0.035)^2C`

and so on

In general after n years

`C(n) = 1.035^n C\\`

When C(n) is twice C we have

`2=1.035^n\\log 2= n log 1.035\\n = 20.14`

Between 20 and 21 years

Hence The electric utities will need to double their generating capacity in about ___20.14__ years.