Explanation:
The exponential function that models this situation is:
[tex]n(t)=n_0(1-r)^t[/tex]Where n(t) is the amount we want to model the decay, n0 is the initial amout, r is the rate of decay and t is the time in years.
For this particular problem we have n0 = 18,000, r = 0.02 and we have to find n(6)
[tex]\begin{gathered} n(t)=18,000(1-0.02)^t \\ n(t)=18,000\times0.98^t \end{gathered}[/tex]When t = 6:
[tex]n(6)=18,000\times0.98^6=15,945.16286[/tex]Answers:
• Function:
[tex]n(t)=18,000\times0.98^t[/tex]Population after 6 years: 15,945
