   Chapter 10.5, Problem 88E Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203

Solutions

Chapter
Section Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203
Textbook Problem

Median Home Prices The median home price in the United States over the period January 2010–January 2015 can be approximated by P ( t ) = 0.4.5 t 2 − 15 t + 180  thousand dollars     ( 0 ≤ t ≤ 5 ) , where t is time in years since the start of 2010.66a. Compute the average rate of change of P ( t ) over the interval [ 1 , 5 ] , and interpret your answer. [HINT: See Example 3 of section 10.4.]b. Estimate the instantaneous rate of change of P ( t ) at t = 1 andinterpret your answer. [HINT: See Example 2 (a).]c. The answer to part (a) and part (b) have opposite signs. What does this indicate about the price?

(a)

To determine

To calculate: The average rate of change of the median price of home in U.S. in time interval [1,5] such that P(t)=4.5t215t+180 thousand dollars where 0t5 and interpret the result.

Explanation

Given information:

The median price of home in U.S. is expressed as P(t)=4.5t215t+180 thousand dollars where 0t5 from the year 2010.

Formula used:

The average rate of change of function f(x) is:

Average rate of change=ΔfΔt

Calculation:

Consider the function for price, P(t)=4.5t215t+180.

Evaluate the change in price from t=1 to t=5

Δp=p(5)p(1)

Evaluate the value of p(1):

P(t)=4.5t215t+180P(1)=4.5(1)215(1)+180=169.5

Evaluate the value of p(5).

P(t)=4

(b)

To determine

To calculate: The instantaneous rate of change of the median price of home in United States at t=1 such that P(t)=4.5t215t+180 thousand dollars here 0t5 and to interpret the result.

(c)

To determine

The explanation why the sign of the average rate of change of the median price of home in time interval [1,5] is positive and rate of change of the median price of home at t=1 is negative.

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