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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 10: Q. 351 (page 1055)

A bacteria doubles its original population in $24$ hours $(A = 2 A_{0})$ . How big will its population be in $72$ hours?

Short Answer

Expert verified

The population becomes eight times

Step by step solution

01

Given information

Given A bacteria doubles its original population in $24$ hours $A = 2 A_{0}$

02

Substitute in the values to get the equation

Substituting, we get

$A = A_{0} e^{k t} 2 A_{0} = A_{0} e^{24 k} e^{24 k} = \frac{2 A_{0}}{A_{0}} e^{24 k} = 2$

03

Take logarithm and solve

Taking logarithm, we get

$\ln e^{24 k} = \ln 2 24 k = \ln 2 k = \frac{1}{24} \ln 2$

The equation is $A = A_{0} e^{t \frac{1}{24} \ln 2}$

04

Substitute the value of t and solve

Substituting, we get

$A = A_{0} e^{72 \frac{1}{24} \ln 2} A = A_{0} e^{3 \ln 2} A = A_{0} e^{\ln 8} A = 8 A_{0}$

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In the following exercises, solve each equation.

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