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

Carly Shannon

Carly Shannon

Answered question

2022-01-29

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.
What is the initial number of bacteria? (round to the nearest whole number of bacteria.)

Answer & Explanation

Howard Gallagher

Howard Gallagher

Beginner2022-01-30Added 13 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
What is the initial number of bacteria?
put t=0 then we have
A(0)=900e0.0593×0
=900e0
=900
initially it will be 900

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