University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 1 - Section 1.5 - Exponential Functions - Exercises - Page 38: 35


The number of bacteria the colony will contain after 24 hours is $2.815\times10^{14}$.

Work Step by Step

A colony of bacteria has 1 bacterium at start and doubles every half an hour. We see right away that the rate of change here is $2$ for every half an hour and the starting number of bacteria is $1$. So, if we take $t$ to be the amount of hours which have passed and $b$ to be the number of bacteria after $t$ hours, we come up with this model to calculate $b$: $$b=1\times(2)^{2t}$$ $$b=4^t$$ Therefore, after $24$ hours, the number of bacteria in the colony would be $$b=4^{24}\approx2.815\times10^{14}$$
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