Price Inflation in the United States is typically about 3% per year. Assuming an annual inflation rate of 3%, do the following:

Question

a.) Create a model that gives the future price of a candy bar that costs $0.75 today.

b.) Determine when the price of the candy bar is expected to reach $1.50.

c.) When the price reaches $1.50, at what instantaneous rate (in dollars per year) will the price of the candy bar be changing?

Please show all work.

Answer 1

a)

F = p (1+0.03)^t

So the model for the future price of a candy bar of $075 is:

F = 0.75(1.03)^t

b)

Now plug 1.50 to F and find the P.

1.5 = .75 (1.03)^t

1.5/.75 = 1.03^t

2 = 1.03 ^ t

Now get log from both sides to solve the equation.

log 2 = t log 1.03 so t = log 2 / log 1.03 which is almost 23.44977 years

c)

Get derivative from the function you got in part a) and plug 23.44977 into t,

dF/dt = 0.75 x 1.03 ^ t x Ln 1.03 = 0.75 x 1.03 ^ 23.44977 x .029559 = 0.044337 which is the rate of change (increase) of the price per year at that time.