A water sample in a laboratory initially contains 6000 bacteria. The organisms reproduce at a rate of 10% per hour. Find the function that corresponds

Harlen Pritchard

Harlen Pritchard

Answered question

2020-10-21

A water sample in a laboratory initially contains 6000 bacteria. The organisms reproduce at a rate of 10% per hour. Find the function that corresponds to this situation. Then predict how long it will take for the population of bacteria to double in number. Round your answer to the nearest hundredth of an hour.

Answer & Explanation

Faiza Fuller

Faiza Fuller

Skilled2020-10-22Added 108 answers

Use the exponential growth function:
y=a(1+r)x
where aa is the initial value and r is the growth rate.
Substitute a=6000 (6000 bacteria) and r=0.1 (from 10% per hour) to find the equation:
y=6000(1+0.1)x
y=6000(1.1)x
Substitute y=12000 (double in number) and solve for x:
12000=6000(1.1)x
Divide both sides by 6000:
2=(1.1)x
Take the natural logarithm of both sides:
ln2=ln(1.1)x
Apply Power Property of logarithms:
ln2=xln1.1
Divide both sides by ln1.1:
ln2ln1.1=x
x≈7.27 hours
Jeffrey Jordon

Jeffrey Jordon

Expert2021-08-10Added 2605 answers

Answer is given below (on video)

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