   Chapter 2, Problem 23RE 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

In Exercises 21-24, use the given information to find an exponential model of the form Q = Q 0 e − k t or Q = Q 0 e k t , as appropriate. Round all coefficients to three significant digits when rounding is necessary.Q is the diameter (in centimeters) of a circular patch of mold on your roommate's damp towel you have been monitoring with morbid fascination. You measured the patch at 2.5 centimeters across 4 days ago and have observed that it is doubling in diameter every 2 days (t is time in days).

To determine

To calculate: The exponential model Q=Q0ekt or Q=Q0ekt where the diameter of the circular patch is Q0=25 cm and the diameter of the circular patch is doubled after every t=2 days.

Explanation

Given Information:

The provide original diameter of a circular patch Q0=25 centimeters and the diameter of a circular patch is doubled after every 2 days.

Formula used:

The exponent property of logarithm:

If a,b>0 and n is any number with a0

lnabn=nlnab

Identity property of logarithm:

logaa=1

Calculation:

Consider the equation Q=Q0ekt.

According to question Q is a double of the original circular patch diameter Q0 therefore, Q=2Q0 then,

Substitute the value Q0=25, Q=5 and t=2 in the equation Q=Q0ekt then simplify,

5=2.5ek2

Divide by 2.5 on both sides then simplify,

52.5=2.5ek22

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