   Chapter 10.6, Problem 51E 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

Ecology Increasing numbers of manatees have been killed by boats off the Florida coast. The following graph shows the relationship between the number of boats registered in Florida and the number of manatees killed each year Boats (100,000)The regression curve shown is given by f ( x ) = 3.55 x 2 − 30.2 x + 81  manatee deaths                                                          ( 4.5 ≤ x ≤ 8.5 ) where x is the number of boats (hundreds of thousands) registered in Florida in a particular year and f ( x ) is the number of manatees killed by boats in Florida that year.80 Compute and interpret f ′ ( 8 ) .

To determine

To calculate: The value of f(8)

for the function f(x)=3.55x230.2x+81, where x represents the number of boats (hundreds of thousands) registered in Florida in a particular year and f(x)

represents the number of manatees killed by boats in Florida that year, also interpret the answer and the graph which shows the relation between the numbers of boats registered in Florida and the number of manatees killed each year is as follows: Explanation

Given information:

The function f(x)=3.55x230.2x+81, where x represents the number of boats (hundreds of thousands) registered in Florida in a particular year and f(x)

represents the number of manatees killed by boats in Florida that year.

The graph which shows the relation between the numbers of boats registered in Florida and the number of manatees killed each year is as follows:

Formula used:

The difference quotient formula is used which is as follows:

f(x)=limh0f(x+h)f(x)h

The square of sum formula as,

(a+b)2=a2+b2+2ab

Calculation:

Consider the function f(x)=3.55x230.2x+81, where x represents the number of boats (hundreds of thousands) registered in Florida in a particular year and f(x)

represents the number of manatees killed by boats in Florida that year.

The difference quotient formula used to estimate the exact value of derivative algebraically is:

f(a)=limh0f(a+h)f(a)h.

Substitute a=8

into the above formula,

f(8)=limh0f(8+h)f(8)h

Substitute the values of f(8)

and f(8+h)

in f(x),

f(8)=limh0[3

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