The exponential decrease (decay) equation is given by:
[tex]P(t)=P_o(1-r)^t[/tex]
Where P is the population at time t, Po is the initial population, and r is the decay rate in decimal form.
We are given the parameters: Po = 24000, r = 10% = 0.10.
Substituting:
[tex]\begin{gathered} P(t)=24000(1-0.10)^t \\ \\ Calculating: \\ \\ P(t)=24000(0.9)^t \end{gathered}[/tex]
We can use the equation to fill up the table. For example, for t = 1:
[tex]\begin{gathered} P(1)=24000(0.9)^1=24000\cdot0.9 \\ \\ P(1)=21600 \end{gathered}[/tex]
Proceeding in a similar way, we can find the rest of the values for t = 2 up to t = 10.
b) Expressing the rule in words, we can find the population in a given year as 0.9 times the population in the previous year, starting at 24000.
c) The recursive formula is:
[tex]\begin{gathered} P(t)=0.9\cdot P(t-1) \\ \\ Where \\ \\ P(0)=24000 \end{gathered}[/tex]
