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 121212 wild turkeys, and their number increases by approximately 40\%40%40, percent each year.
At the first year Sheila counted 181818 white-tail deer, and their number increases by 101010 additional deer per year.
What is the first year in which Sheila counts more turkeys than deer?

The 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: , 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.

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:

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

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

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.

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