   Chapter 10.5, Problem 87E 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

Crude Oil Prices The price per barrel of crude oil in constant 2008 dollars can be approximated by P ( t ) = 0.45 t 2 − 12 t + 105  dollars     ( 0 ≤ t ≤ 28 ) , where t is time in years since the start of 1980.a. Compute the average rate of change of P ( t ) over the interval [ 0 , 28 ] , and interpret your answer. [HINT: See Example 3 of section 10.4.]b. Estimate the instantaneous rate of change of P ( t ) at t = 0 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 of oil?

(a)

To determine

To calculate: The average rate of change of the price of crude oil per barrel in time interval [0,28] such that P(t)=0.45t212t+105 where t is time in years 0t28 and interpret the result.

Explanation

Given information:

The crude oil price is expressed as P(t)=0.45t212t+105 and 0t28, the year starts from 1980.

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)=0.45t212t+105.

Evaluate the change in price from t=0 to t=28

Δp=p(28)p(0)

Evaluate the value of p(0).

P(t)=0.45t212t+105P(0)=0.45(0)212(0)+105=105

Evaluate the value of p(28)

(b)

To determine

To calculate: The instantaneous rate of change of the price of crude oil per barrel at t=0 such that P(t)=0.45t212t+105 here 0t28 and interpret the result.

(c)

To determine

The explanation why the average rate of change of the price of crude oil in part (a) is positive and negative in part (b).

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