   Chapter 10.1, Problem 52E 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

Funding for NASA up to 1966 (Compare Exercise 51.) The percentage of the U.S. federal budget allocated to NASA from 1958 to 1966 can also be modeled by p ( t ) = 4.5 1.07 ( t − 8 ) 2  percentage points (t is time in years since 1958).a. Numerically estimate lim x → + ∞ p ( t ) , andinterpret the answer. [HINT: See Example 6.]b. How does your answer to part (a) compare with actual current funding for NASA?

(a)

To determine

To calculate: The value of limt+p(t) for the function p(t)=4.51.07(t8)2, where t is the time in years since 1958 with the function representing the percentage of the U.S. federal budget allocated to NASA from 1958 to 1966 and also interpret the answer.

Explanation

Given Information:

The function p(t) represents the percentage of the U.S. federal budget allocated to NASA from 1958 to 1966 and the function is as follows:

p(t)=4.51.07(t8)2

Formula used:

The limit limxf(x) exists when x approaches to +, f(x) converges to a finite point or diverges to infinity.

Calculation:

Consider the expression, limt+p(t)

Where, p(t)=4.51.07(t8)2

Substitute t=0 in p(t)=4.51.07(t8)2:

p(0)=4.51.07(08)2=4.5(1.07)64=4.575.955945=0.592

Substitute t=10 in p(t)=4.51.07(t8)2:

p(10)=4.51.07(108)2=4.5(1.07)4=4.51.3107=3.43303

Substitute t=20 in p(t)=4.51.07(t8)2:

p(20)=4.51.07(208)2=4.5(1

(b)

To determine

The comparison of actual current funding of NASA with the one that is obtained in part (a).

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