Exponential Growth and Decay Exponential growth and decay problems follow the model given by the

Turnseeuw

Turnseeuw

Answered question

2022-01-30

Exponential Growth and Decay
Exponential growth and decay problems follow the model given by the equation A(t)=Pert
-The model is a function of time t
-A(t) is the amount we have ater time t
-PIs the initial amount, because for t=0, notice how A(0)=Pe0×t=Pe0=P
-Tis the growth or decay rate. It is positive for growth and negative for decay
Growth and decay problems can deal with money (interest compounded continuously), bacteria growth, radioactive decay. population growth etc.
So A(t) can represent any of these depending on the problem.
Practice
The growth of a certain bactenia population can be modeled by the function
A(t)=900e0.0534
where A(t) is the number of bacteria and t represents the time in minutes.
How long will t take for the number of bacteria to double? (your answer must be accurate to at least 3 decimal places.)

Answer & Explanation

stamptsk

stamptsk

Beginner2022-01-31Added 23 answers

Given
The growth of a certain bacteria population can be modeled by the function
where A(t) is the number of bacteria and t represents the time in minutes
Explanation: we have function A(t)=900e0.0593t
How long will it take or the number of bacteria to double?
2P=Pe0.0593t
2=e0.0593t
taking log on both sides then we have
log2=0.0593 t
t=0.0593log2
=0.05930.6931
=0.0855

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