Answer:
Approximately after 66.15 years, there will be 100 coyotes left
Step-by-step explanation:
We can use the formula [tex]F=P(1+r)^t[/tex] to solve this.
Where
F is the future amount (F=100 coyotes)
P is the initial amount (P=750 coyotes)
r is the rate of decrease per year (which is -3% per year or -0.03)
t is the time in years (which we need to find)
Putting all the information into the formula we solve.
Note: The logarithm formula we will use over here is [tex]ln(a^b)=bln(a)[/tex]
So, we have:
[tex]F=P(1+r)^t\\100=750(1-0.03)^t\\100=750(0.97)^t\\\frac{100}{750}=0.97^t\\\frac{2}{15}=0.97^t\\ln(\frac{2}{15})=ln(0.97^t)\\ln(\frac{2}{15})=tln(0.97)\\t=\frac{ln(\frac{2}{15})}{ln(0.97)}\\t=66.15[/tex]
Hence, after approximately 66.15 years, there will be 100 coyotes left.
Rounding, we will have 66 years
