Question

The data in the table represents the predicted price of a gallon of milk, y, for number of years, x.

A 2-column table with 5 rows. The first column is labeled years with entries 0, 1, 2, 3, 4. The second column is labeled price (dollar sign) with entries 3.00, 3.12, 3.24, 3.37, 3.51.

Which form of an equation was used to model the price of a gallon of milk?

y = ax + b
y = ax2 + b
y = abx
y = a + bx

Answer 1

The exponential form y = ab^x.

Reason: y(0) = 3 so a = 3, and successive ratios y(x+1)/y(x) ≈ 1.04, so y ≈ 3(1.04)^x (3(1.04)^1 = 3.12, 3(1.04)^2 ≈ 3.2448, etc.). The differences are not constant, so a linear form does not fit.