Answer:
Using the formula:
[tex]P = P_0(1+r)^t[/tex] .....[1]
where,
P is the population after t years
[tex]P_0[/tex] is the initial population
r is the rate (in decimal)
As per the statement:
A population of 80,000 toads is expected to shrink at a rate of 9.2% per year.
⇒Initial population([tex]P_0[/tex]) = 80,000 toad
and
r = -9.2% = -0.092
We have to find the toad population be in 20 years.
t = 20 years
Substitute the given values in [1], we have;
[tex]P = 8000 \cdot (1-0.092)^{20}[/tex]
⇒[tex]P = 8000 \cdot (0.908)^{20} = 80000 \cdot 0.145116559[/tex]
Simplify:
[tex]P = 11609.3247 \approx 11609[/tex]
Therefore, about 11609 will be the toad population be in 20 years.
