Answer:
7th year.
Step-by-step explanation:
We have been given that at the first year Sheila counted 12 wild turkeys, and their number increases by approximately 40% each year.
We can see that the number of turkeys is increasing exponentially. Since an exponential function is in form: [tex]y=a*b^x[/tex], where,
y = Amount after x years.
a = Initial value or amount.
b = Rate; for growth, rate is in form 1+r, where r is in decimal form.
Upon substituting our given values we will get number of turkeys, T(n), where n is the number of years after first year.
[tex]T(n)=12*(1+0.40)^n[/tex]
[tex]T(n)=12*(1.40)^n[/tex]
We are also told that at the first year Sheila counted 18 white-tail deer, and their number increases by 10 additional deer per year.
We can see that change in number of deer is linear, so number of deer D(n) after n+1 years will be: [tex]D(n)=10n+18[/tex]
Let us equate both functions to find the number of years, when number of turkeys will be equal to number of deer.
[tex]12*(1.40)^n=10n+18[/tex]
Upon solving our equation by online calculator, we will get,
[tex]n=5.27169[/tex]
The least possible value of n is 6. Therefore, number of years after first year is 6. Hence, total number of years after which # of turkeys is more than the # of deer for the first time is 7.
Therefore, in 7th year Sheila will count more turkeys than deer.
