Question

Let's Try it out (2 Steps)The population of a once very popular city of 250,000people has been decreasing by 3.5% each year,Write an exponential decay function that represents thepopulation after t years,y = a[1 – r)'250,000(1 - 3.5)Simplify!250,000(.035)Use your model to approximate what the population willbe 7 years from now.*Round answer to the nearest WHOLE number

Answer 1

The population at the onset as 250,000. There has been a 3.5% decrease every year.

The exponential decay function therefore is;

$\begin{gathered} y=a(1-r)^t \\ a=250000,r=0.035,t=\text{time in years} \end{gathered}$

Hence, to approximate what the population would be 7 years from now;

$\begin{gathered} y=a(1-r)^t \\ y=250000(1-0.035)^7 \\ y=250000(0.965)^7 \\ y=250000\times0.779275\ldots \\ y=194818.9516 \\ y\approx194819\text{ (to the nearest whole number)} \end{gathered}$

The population after 7 years shall be 194,819 people (rounded to the nearest whole number).