   Chapter 11.1, Problem 90E 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 Price The median home price in the United States over the period Jannuary 2015 can be approximated by P ( t ) = 4.5 t 2 − 15 t + 180  thousnad dollars .    ( 0 ≤ t ≤ 5 ) . Where t is time in years since the start of 2010. Find P ′ ( t ) and P ′ ( 1 ) . What does the second answer tell you about the price of crude oil? [HINT: See Example 2.]

To determine

To calculate: The derivative P(t) and P(1). Also determine the meaning of derived value of P(30) in terms of home prices.

Explanation

Given Information:

A function of median home prices is P(t)=4.5t215t+180 thousand dollars, t is time period between January 2010-January 2015 and it lies in the range 0t5.

Formula used:

Sum and difference rule of derivative is [f±g](x)=f(x)±g(x).

Constant multiple rule is f(cx)=cf(x), where c is any constant.

Derivative of a constant is 0.

Power rule for the function f(x)=xn is f(x)=nxn1 where n is any constant.

Calculation:

Consider the provided function, P(t)=4.5t215t+180,

Apply sum and difference rule of derivative to the function P(t)=4.5t215t+180 with respect to t.

P(t)=ddt(4.5t2)ddt(15t)+ddt(180)

Apply constant multiple rule,

P(t)=4

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