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Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203

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Chapter
Section
BuyFindarrow_forward

Finite Mathematics and Applied Cal...

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

Lobsters Marjory Duffin, CEO of Duffin House, is particularly fond of having steamed lobster at working lunches with executives from OHaganBooks.com and is therefore alarmed to learn that the yearly lobster harvest from New York’s Long Island Sound has been decreasing dramatically since 1997. Indeed, the size of the annual harvest can be approximated by

n ( t ) = 9.1 ( 0.81 t ) millionpounds, where t is time in years since 1997.59

a. The model tells us that the harvest was ______ pounds in 1997 and decreasing by _______% each year.

b. What does the model predict for the 2013 harvest?

(a)

To determine

To fill: The correct words in the statement “The model tells us that harvest was _____ million pound in 1997 and decreasing by ____ % each year”

Explanation

Given Information:

The size of the annual harvest can be approximated by the expression,

n(t)=9.1(0.81)t

Here, t is the time in year since 1997 and n(t) is in million pounds.

Consider the expression of the annual harvest is,

n(t)=9.1(0.81)t

To find the harvest in 1997, substitute t=0 in the expression n(t)=9.1(0.81)t.

n(t)=9.1(0.81)0=9.1

Thus, annual harvest in 1997 was 9.1 million.

Now substitute t=1 in the expression n(t)=9.1(0.81)t

n(t)=9

(b)

To determine

The annual harvest in 2013 if the size of the annual harvest can be approximated by the expression n(t)=9.1(0.81)t. Here, t is the time in year since 1997 and n(t) is in million pounds.

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