Chapter 11, Problem 31RE

### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

Chapter
Section

### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# Inflation The impact of inflation on a $60,000 pension can be measured by the purchasing power P of$60,000 after t years. For an inflation rate of 5% per year, compounded annually, P is given by P = 60 , 000 e 0.0488 t At what rate is purchasing power changing when t = 10?(Source: Viewpoints, VALIC)

To determine

To calculate: The rate of change of purchasing power P at t=10 if impact of inflation on a $60,000 pension can be measured by purchasing power P of$60,000 after t years for an inflation rate 5% per year compounded annually purchasing power P is given by the function P=60000e0.0488t.

Explanation

Given Information:

The impact of inflation on a $60,000 pension can be measured by purchasing power P of$60,000 after t years for an inflation rate 5% per year compounded annually purchasing power P is given by the function P=60000e0.0488t.

Formula used:

Chain rule:

if f and g are differentiable function with y=f(u), and u=g(x), then y is a differentiable function of x, and

dydx=dydududx

The derivative of function f(x)=e(ax+b) is given by;

f(x)=e(ax+b)(a)

And derivative of constant function is zero.

Calculation:

Consider the purchasing power P is given by the function,

P=60000e0.0488t

Where t it the number of years

The rate of change of purchasing power P is given by;

P(t)=ddt(60000e0

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