A colony of bacteria with an initial population of 3000

Zerrilloh6

Zerrilloh6

Answered question

2022-01-19

A colony of bacteria with an initial population of 3000 grows over time t (in hours) at a rate of 22% per hour.
a). Use the growth rate to write an exponential function to model the growth.
b). How long does it take for the population to double?

Answer & Explanation

Mason Hall

Mason Hall

Beginner2022-01-19Added 36 answers

We use here simple exponential growth and decay function to solve these problems.
Solution:
According to question
P0=3000
Rate(γ)=22%=22100=0,22,
Time=t
a) P=3000×e0,22×t (Exponential form for growth P=P0eγt)
P=3000e0,22t *
b) when population double then P=6000put in esn *
6000=3000e0,22t
60003000=e0,22t
on solving using natural logarithm then
t=3×190669
t=3×19 hours (approx)

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