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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. 445 (page 1066)

Mouse populations can double in 8 months $(A = 8 A_{0})$ . How long will it take for a mouse
population to triple?

Short Answer

Expert verified

It will approx take $12.7$ months.

Step by step solution

01

Step 1. Given information

$A = 2 A_{0} t = 8 m o n t h s$

02

Step 2. Writing the concept.

An amount $A_{0}$ that grows or decays at rate k for certain time t, will be given by

$A = A_{0} e^{k t}$

03

Step 3. Calculation

Put the values of respective variables in the given formula:

$A = 2 A_{0} t = 8 2 A_{0} = A_{0} e^{8 k} e^{8 k} = \frac{2 A_{0}}{A_{0}} e^{8 k} = 2 T a k i n g n a t u r a l \log b o t h s i d e s, \ln e^{8 k} = \ln 2 8 k . \ln e = \ln 2 k = \frac{1}{8} \ln 2 N o w s u b s t i t u t e A = 3 A_{0} 3 A_{0} = A_{0} e^{t \frac{1}{8} \ln 2} e^{t \frac{1}{8} \ln 2} = \frac{3 A_{0}}{A_{0}} e^{t \frac{1}{8} \ln 2} = 3 T a k i n g \log b o t h s i d e s \ln e^{t \frac{1}{8} \ln 2} = \ln 3 (t \frac{1}{8} \ln 2) \ln e = \ln 3 t = \frac{\ln 3}{t \frac{1}{8} \ln 2} t 鈮� 12.7$

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