Original Number of trees = P₀ = 40,000
Rate of decrease = r = 10% = 0.10
We want to find when the number of trees will be one quarter of the original number. One quarter can be expressed as 25%, so we want to find when the number of trees is 25% of P₀ .
Using the given equation, we can write:
[tex]P= P_{o}(1-r)^{t} \\ \\
0.25 P_{o}=P_{o}(1-0.1)^{t} \\ \\
0.25= (0.9)^{t} \\ \\
log(0.25)=log((0.9)^{t}) \\ \\
log(0.25)=t*log(0.9) \\ \\
t= \frac{log(0.25)}{log(0.9)} \\ \\
t=13.1[/tex]
Thus, in approximately 13 years, the number of trees in the city will be reduced to a quarter of the original amount.
