Question

The population of a city grows exponentially at rate of 8% per year.Find the number of years it takes for the population to be doubled Give your answer correct to the nearest whole number

Answer 1

It will take 9 years for the population to double

Explanation:

Exponential Growth

The natural growth of some magnitudes can be modeled by the equation:

`P=P_o(1+r)^t`

Where P is the actual amount of the magnitude, Po is its initial amount, r is the growth rate and t is the time.

The population of a city grows at a rate of r=8% = 0.08 per year. We are required to find when (t) the population will double, or P=2Po.

Substituting in the equation:

`2P_o=P_o(1+0.08)^t`

Simplifying:

`2=(1.08)^t`

Taking logarithms:

`\log 2=\log (1.08)^t`

Applying the exponent property of logs:

`\log 2=t\log (1.08)`

Solving for t:

`\displaystyle t=(\log 2)/(\log (1.08))`

Calculating:

`t\approx 9`

It will take 9 years for the population to double