Algebra homework

Question

In a certain candy factory, the amount of candy cars produced annually is double the amount from the year before. This relationship can be described by:

A. A exponential function

B. Neither a linear nor exponential function

C. A linear function

D. Both a linear and exponential function

Answer 1

To answer this one, you can begin by writing the facts given to you in a mathematical equation that describes candy cars produced in any given year, X_n, where n is the year of interest_.

X_n = 2X_n-1, where n >0

Substitute n = 1, 2, 3 etc as below and observe the developing relationship between X_n and n

X₁ = 2.X₀

X₂ = 2.X1 = 2².X₀

X₃ = 2.X2 = 2³.X₀

Now generalize the observed pattern

X_n = 2ⁿ.X₀

Clearly the growth in the number of candies each year is not a linear function of 'n'. It is an exponential growth function.