Question

Need help asap!..The population of a city is 100,000 and grows at a rate of 4%, four times per year. How big will the population be in 4 years?

Answer 1

187,298.

Step-by-step explanation:

The equation that model the growth in the city is an exponential function with the form:

`P=P_0\cdot(1+r)^t`

Where P0 is the initial population, r is the growth rate and t is the number of quarters because the rate applies four times per year.

So, replacing P0 by 100,000, r by 4%, and t by 16 quarter ( 4 years x 4 quarters), we get:

`\begin{gathered} P=100000\cdot(1+0.04)^(16) \\ P=100000\cdot1.8729_{} \\ P=187,298.1246 \end{gathered}`

Therefore, after 4 years, the population of the city will be 187,298.