Explanation Given: The following table shows for a tubeworm the rate of growth in length, measured in meters per year, at the given length, in meters, Length in Meters Growth rate in meters per year 0 0.0510 0.5 0.0255 1.0 0.0128 1.5 0.0064 2.0 0.0032 Table ( 1 ) Approach: The model is considered to be exponential if the successive ratios are equal. Successive ratio = New value old value The expression for an exponential decay model is, New value = initial value × ( decay factor ) t …… ( 1 ) The decay rate is given by, r = 1 − a …… ( 2 ) Here, a is the growth factor and r is growth rate. Calculation: The successive ratios are shown in below table. Length Increment Successive differences Successive Ratios 0 to 0.5 0.0255 − 0.0510 = − 0.026 0.0255 0.0510 = 0.500 0.5 to 1.0 0.0128 − 0.0255 = − 0.013 To determine (b) To find: The functional notation for the growth rate at a length of 0.64 meters and its value.

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

6th Edition

ISBN: 9781337111348

Author: Bruce Crauder, Benny Evans, Alan Noell

Publisher: Cengage Learning

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Chapter 4.3, Problem 20E

To determine

(a)

The more appropriate model for the tubeworm and the model and the percentage growth rate.

To determine

(b)

To find:

The functional notation for the growth rate at a length of 0.64 meters and its value.

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Chapter 4.3, Problem 19E

Chapter 4.3, Problem 1SBE

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Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

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(a) The more appropriate model for the tubeworm and the model and the percentage growth rate.

Solution Summary: The author explains that the exponential model is more suitable for the data and the percentage decay rate per meter is 75%.