Answer:
Approximately after 66.15 years, there will be 100 coyotes left
Step-by-step explanation:
We can use the formula
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.
<u>Note:</u> The logarithm formula we will use over here is ![ln(a^b)=bln(a)](https://tex.z-dn.net/?f=ln%28a%5Eb%29%3Dbln%28a%29)
So, we have:
![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](https://tex.z-dn.net/?f=F%3DP%281%2Br%29%5Et%5C%5C100%3D750%281-0.03%29%5Et%5C%5C100%3D750%280.97%29%5Et%5C%5C%5Cfrac%7B100%7D%7B750%7D%3D0.97%5Et%5C%5C%5Cfrac%7B2%7D%7B15%7D%3D0.97%5Et%5C%5Cln%28%5Cfrac%7B2%7D%7B15%7D%29%3Dln%280.97%5Et%29%5C%5Cln%28%5Cfrac%7B2%7D%7B15%7D%29%3Dtln%280.97%29%5C%5Ct%3D%5Cfrac%7Bln%28%5Cfrac%7B2%7D%7B15%7D%29%7D%7Bln%280.97%29%7D%5C%5Ct%3D66.15)
Hence, after approximately 66.15 years, there will be 100 coyotes left.
Rounding, we will have 66 years