A population of bacteria is initially 6000. After three hours the population is

facas9

facas9

Answered question

2021-09-26

A population of bacteria is initially 6000. After three hours the population is 3000.
If this rate of decay continues, find the exponential function that represents the size of the bacteria population after t hours. Write your answer in the form f(t)=a(b)t.
Use either fractions, or decimals rounded to 4 places

Answer & Explanation

Arnold Odonnell

Arnold Odonnell

Skilled2021-09-27Added 109 answers

Step 1
Given, A population of bacteria is initially 6000. After three hours the population is 3000.
We know that, the exponential function is given as
P=P0ert
where P0 is the initial value
r is the rate
P is the total value
t is time
Step 2
Now, Initial value, P0=6000
P=3000
t=3
The exponential function becomes
3000=6000e3r
12=e3r
using ln on both sides,
ln(0.5)=ln(e3r)
ln(0.5)=3rlog(e)
ln(0.5)=3r
ln(0.5)3=r
r=0.2310
The exponential function that represents the size of the bacteria population after t hours.
is given as
P=6000e.2310t

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