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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. 350 (page 1055)

A virus takes $6$ days to double its original population $(A = 2 A_{0})$ . How long will it take to triple its population?

Short Answer

Expert verified

The time taken is $9.5$ days

Step by step solution

01

Given information

Given A virus takes 6 days to double its original population $A = 2 A_{0}$

02

Substitute in the values to get the equation

Substituting, we get

$A = A_{0} e^{k t} 2 A_{0} = A_{0} e^{6 k} e^{6 k} = \frac{2 A_{0}}{A_{0}} e^{6 k} = 2$

03

Take logarithm and solve

Taking logarithm, we get

$\ln e^{6 k} = \ln 2 6 k 路 \ln e = \ln 2 k = \frac{1}{6} \ln 2$

The equation is $A = A_{0} e^{t - \frac{1}{6} \ln 2}$

04

Substitute A=3A0 and solve

Substituting, we get

$3 A_{0} = A_{0} e^{\frac{1}{6} \ln 2} e^{\frac{1}{6} \ln 2} = \frac{3 A_{0}}{A_{0}} e^{t \frac{1}{6} \ln 2} = 3$

05

Take logarithm and solve

Taking logarithm, we get

$\ln e^{t . \frac{1}{6} \ln 2} = \ln 3 t . \frac{1}{6} \ln 2 = \ln 3 t = 9.5$

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