With yearly inflation of 8 % , prices are given by P = P 0 ( 1.08 ) t , where P 0 is the price in dollars when t = 0 and t is time in years. Suppose P 0 = 1 . How fast (in cents/year) are prices rising when t = 1 0 ? Round your answer to two decimal places.

by 16.61 cents per year

Explanation:

P = Po(1.08)^t

How fast are prices increasing?

The rate of increase:

dP/dt = d/dt(Po(1.08)^t)

= d/dt((1.08)^t)

We use derivative formula of exponential function as we continue solving this problem

dP/dt = (1.08)^t x ln(1.08)

dP/dt = ln(1.08)x(1.08)^t

Now t value = 10,

P'(10) = ln(1.08)x(1.08)^10

= 0.07696x2.1589

= 0.1661 dollars and 16.61 cents per year

In conclusion, prices are rising by 16.61 cents per year.

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