The cost C of a pound of margarine in 2006 was 66 cents. in 2010 the cost was 83 cents. Assuming the exponential growth model applies:

Question

A) Find the exponential growth rate to the nearest tenth of a percent, and write the equation

B) Find the cost of a pound of margarine in 2012 and 2018

Answer 1

a_n = a₁(r)ⁿ, where a₁ = original amount, r = rate, t = time

83 = 66(r)⁴

1.258 ≈ r⁴

1.05 ≈ r

 

a_6 ≈ 66(1.05)⁶

a₆ ≈ 66(1.34)

a₆ ≈ 88.44

 

Do the same calculation for n = 12.

Answer 2

Assuming that you are looking for an exponential equation of the form C=ab^n where n is the number of years after 2006 (year zero), then the equation can be easily determined using the STAT mode on a TI-84 Plus calculator using exponential regression as C=0.66*1.059^n. (b has been rounded)

 

When you plug in n=6, the cost in 2012 would be 93 cents. The cost in 2018 (n=12) would be 131 cents.

 

Learning to use your calculator efficiently is a skill worth cultivating!