EBK PRECALCULUS W/LIMITS
EBK PRECALCULUS W/LIMITS
4th Edition
ISBN: 9781337516853
Author: Larson
Publisher: CENGAGE CO
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Chapter 3, Problem 112RE
To determine

To find: Population of bats one year ago.

Expert Solution & Answer
Check Mark

Answer to Problem 112RE

Population of species of bat one year ago was B=1242 .

Explanation of Solution

Given:

Exponential decay model

  B= B0ekt

Consider an exponential decay model

  B= B0ekt

Where B is the number of species of bat at present, B0 is the minimum intensity for comparison, k is constant, and t is the years.

Before 5 years (t=–5) the numbers are 2000.

Implies

  2000= B0e−5kB0e−5k=2000

Hence B0e−5k=2000 ......(1)

Before 2 years (t=–2) the numbers are 1400

Implies

  1400= B0e−2kB0e−2k=1400

Hence B0e−2k=1400 ......(2)

Divide equation (2) by equation (1)

  B0e−5k=2000B0e−2k=1400e−5k+2k=1.428e−3k=1.428

Applying natural logarithm on both sides

  ln e–3k= ln1.428–3k lne =0.356k=–0.3563k=–0.119

Substituting the value of k in equation (1)

  B0e−5(−0.119)=2000B0e0.595=2000B0= 20001.813B0=1103.144

Therefore, the model is B0=1103.144e(−0.119)t

Hence, one year ago (t=–1) the number of species was

  B0=1103.144e(−0.119)t=1103.144×1.126  =1242.55

Hence, population of species of bat one year ago was B=1242 .

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Chapter 3, Problem 111RE
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Chapter 3, Problem 113RE

Chapter 3 Solutions

EBK PRECALCULUS W/LIMITS

Ch. 3.1 - Prob. 1ECh. 3.1 - Prob. 2ECh. 3.1 - Prob. 3ECh. 3.1 - Prob. 4ECh. 3.1 - Prob. 5ECh. 3.1 - Prob. 6ECh. 3.1 - Prob. 7ECh. 3.1 - Prob. 8ECh. 3.1 - Prob. 9ECh. 3.1 - Prob. 10E
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Prob. 64ECh. 3.5 - Prob. 65ECh. 3.5 - Prob. 66ECh. 3 - Prob. 1RECh. 3 - Prob. 2RECh. 3 - Prob. 3RECh. 3 - Prob. 4RECh. 3 - Prob. 5RECh. 3 - Prob. 6RECh. 3 - Prob. 7RECh. 3 - Prob. 8RECh. 3 - Prob. 9RECh. 3 - Prob. 10RECh. 3 - Prob. 11RECh. 3 - Prob. 12RECh. 3 - Prob. 13RECh. 3 - Prob. 14RECh. 3 - Prob. 15RECh. 3 - Prob. 16RECh. 3 - Prob. 17RECh. 3 - Prob. 18RECh. 3 - Prob. 19RECh. 3 - Prob. 20RECh. 3 - Prob. 21RECh. 3 - Prob. 22RECh. 3 - Prob. 23RECh. 3 - Prob. 24RECh. 3 - Prob. 25RECh. 3 - Prob. 26RECh. 3 - Prob. 27RECh. 3 - Prob. 28RECh. 3 - Prob. 29RECh. 3 - Prob. 30RECh. 3 - Prob. 31RECh. 3 - Prob. 32RECh. 3 - Prob. 33RECh. 3 - Prob. 34RECh. 3 - Prob. 35RECh. 3 - Prob. 36RECh. 3 - Prob. 37RECh. 3 - Prob. 38RECh. 3 - Prob. 39RECh. 3 - Prob. 40RECh. 3 - Prob. 41RECh. 3 - Prob. 42RECh. 3 - Prob. 43RECh. 3 - Prob. 44RECh. 3 - Prob. 45RECh. 3 - Prob. 46RECh. 3 - Prob. 47RECh. 3 - Prob. 48RECh. 3 - Prob. 49RECh. 3 - Prob. 50RECh. 3 - Prob. 51RECh. 3 - Prob. 52RECh. 3 - Prob. 53RECh. 3 - 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