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A population of bacteria in a lab, p(t), can be modeled by the function p(t)=500(0.80)t, where t represents the number of days since the population was first counted. Explain what 500 and0.80 represent in the context of the problem

Answer :

JeanaShupp

Answer: Initial population = 500

Decay factor of population =0.80

Step-by-step explanation:

We know that , the general exponential function is given by :-

[tex]f(t)=Ab^x[/tex] ...(i)

Where , A = initial value

b= growth factor ( if b>1)

or b= decay factor  ( if b<1)

x= Time perid

Given : A population of bacteria in a lab, p(t), can be modeled by the function [tex]p(t)=500(0.80)^t[/tex], where t represents the number of days since the population was first counted.

By comparing [tex]p(t)=500(0.80)^t[/tex] to (i) , we get

[tex]A=500\text{ and } b=0.80[/tex]

i..e Initial population = 500

Also as 0.80<1 , therefore we have decay factor of population =0.80

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