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

7

Explanation:

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Answer 2

7th year.

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.