Answer :
The Solution:
Given that the population of Slim Chance is described by the exponential function below:
[tex]P(t)=40000(0.94)^t\ldots\text{eqn}(1)[/tex]We are required to find the rate at which the population is changing, and also give a numerical rate of change in the population.
By formula, the exponential function is:
[tex]\begin{gathered} P(t)=p_0(1-r)^t\ldots eqn(2) \\ \text{where r=rate (\%)} \end{gathered}[/tex]Comparing eqn(1) and eqn(2), we have that:
[tex]1-r=0.94[/tex]Solving for r in the above equation, we get
[tex]\begin{gathered} r=1-0.94 \\ r=0.06\text{ } \\ \text{ So, to convert to percentage, we multiply by 100 to get,} \\ r=0.06\times100=6\% \end{gathered}[/tex]To find the numerical rate of change in the population, we get
[tex]\text{ Rate of change in the population = 6\% of 40000}=0.06\times40000=2400[/tex]Therefore, the population decreases by 2400 people every year.
