Question

Sheila is a wildlife biologist. At the beginning of each year, she tracks the wild turkey and white-tail deer population in the game reserve where she works. At the first year Sheila counted 12 wild turkeys, and their number increases by approximately 40% each year. At the first year Sheila counted 18 white-tail deer, and their number increases by 10 additional deer per year. What is the first year in which Sheila counts more turkeys than deer?

Answer 1

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: $y=a*b^x$, 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.

$T(n)=12*(1+0.40)^n$

$T(n)=12*(1.40)^n$

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: $D(n)=10n+18$

Let us equate both functions to find the number of years, when number of turkeys will be equal to number of deer.

$12*(1.40)^n=10n+18$

Upon solving our equation by online calculator, we will get,

$n=5.27169$

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.