Question

A researcher determined the amount of ducks that were in a pond over a four-year time span. The results are shown in the table below.YearDucks1642783924106Select an equation that best models the amount of ducks (d) that will be in the pond during the nth year.

Answer 1

The amount by which the ducks increase every year is

$\frac{78-64}{2-1}=14$

And if we call n the number of years, then we know that at n = 1, a = 64 and at n = 2. a = 64 + 14 = 72; therefore, the equation we are seeking must have these properties; therefore, our guess is at the function

$a_n=64+14n$

the above equation is not quite right because it gives a = 64 at n = 0, whereas we want a = 64 at n = 1; therefore, we make the following medication

$a_n=64+14(n-1)$

the n - 1 term ensure that we get a = 64 at n = 1.

Hence, our correct answer choice is the third choice in the column.