Question

A graphing calculator is recommended.

Solve the following exercise on a graphing calculator by graphing an appropriate exponential function (using x for ease of entry) together with a constant function and using INTERSECT to find where they meet. You will have to choose an appropriate window. (Round your answers to one decimal place.)

At 3% inflation, prices increase by 3% compounded annually.

(a) How soon will prices double?
  yr

(b) How soon will prices triple?
  yr

Answer 1

Use y= (1.03)x on the graphing calculator and the graph you will get will be of this type. It will show the price level on y- axis and the number of years on x-axis. You can mark the point corresponding to price level 2 representing doubling of price level and the corresponding number of years on x-axis to know the number of years after which the price level doubles at inflated rate of 3%. Repeat the same excercise for triple price level. The answers you will get are also solved algebrically below.

Suppose,

Initial Price Level = $ P

Inflation rate = r = 3% or 0.03

Number of years = n

a) Number of years in which prices will double

=> 2P = P(1+r)n

=> 2P = P(1+0.03)n

=> n = 23.45 years

b) Number of years in which prices will double

=> 3P = P(1+r)n

=> 3P = P(1+0.03)n

=> n = 37.17 years

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