The initial population of a town is 2900​, and it grows with a doubling time of 17 years. Determine how long it will take for the population to quadruple.

Answer 1

The first value is the "initial value". The population will double every 17 years.

After 17 years (x) the population will be 5800

So, 2900*2^17/17 = 2900 * 2 = 5800

You use rules of logs to calculate what is the value of x, the number of years it will take to quadruple the 2900 population to 11600.

11600 = 2900*2^x/17

divide both side by 2900

4 = 2^x/17

log 4 = log 2^x/17

log 4 = (x/17) log 2

divide both sides by log 2

2 = x/17

multiply both sides by 17

x = 34

2900*2^34/17=11600 (quadruple the initial population)