With a yearly inflation rate of 8 percent, prices are described by P=Q(1.08)^t. Where Q is the price in?

Question

dollars when t = 0 and t is time in years. Suppose Q =1. How fast (in cents/year) are prices rising when t = 10?

Answer 1

OK

1.08 ^ 10 = 2.159

So prices will more than double. With 8% inflation, after 10 years, something costing $1 before would cost $2.16 with this model.

Hope that helps.

Answer 2

Take the first derivative of P(t) -- then plug in t = 10.

To do this, you may need to know that 1.08^t = e^(t*ln(1.08))

So -- the derivative is:

Q*e^(t*ln(1.08)) * ln(1.08) = Q * 1.08^t * ln(1.08)

Plug in Q=1 and t = 10 and you get:

Rate of change = (1.08^10) * ln(1.08) = 0.166153

Since this is in dollars and you want cents, multiply by 100 to get an answer of 16.6153 cents