Question

The sales totals at Macy's food store have increased exponentially over the months. Which of these best shows the sales in the first three months?

A:$1200 in the first month, $1220 in the second month, $1240 in the third month B:$1200 in the first month, $1272 in the second month, $1344 in the third month C:$1200 in the first month, $1285 in the second month, $1370 in the third month D:$1200 in the first month, $1224 in the second month, and $1248.48 in the third month

Answer 1

D

Explanation:

Answer 2

An exponential or geometric function can be expressed as a power of t, where t is time.

This means that if you can fit all three values into the formula

S = S0 * (1+r)^t

for a constant r, and t=1, 2, 3 (or 0, 1, 2 for simplicity), then it's exponential.

You can see right away that the first and second sets of numbers are not exponential. These are linear, because each month is a fixed value greater than the previous one.

If you look at the formula above, you can see that each successive time interval's growth can be calculated by multiplying a fixed value to the previous intervals. For example, the second month is given by:

S(1) = S0 * (1+r)

S(2) = S0 * (1+r)^2 = S0 * (1+r) * (1+r) = S(1) * (1+r)

Since each month's sales is 102% the previous month's in the fourth set, this is the one you want.