Question

A city's population is currently 550,000. if the population doubles every 52 year, what will the population be 208 years from now??

Answer 1

this process is modeled by the next formula:

`P(t)=P_0(2)^{(t)/(t2)}`

where P(t) is the population after time t, P0 is the initial population, and t2 is the time needed by the population to double.

Substituting with P0 = 550,000, t = 208, and t2 = 52, we get:

`\begin{gathered} P(t)=550,000(2)^{(208)/(52)} \\ P(t)=550,000(2)^4 \\ P(t)=550,000\cdot16 \\ P(t)=8,800,000 \end{gathered}`

The population will be 8,800,000