Question

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 1

Answer: Initial population = 500

Decay factor of population =0.80

Explanation:

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

`f(t)=Ab^x` ...(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
`p(t)=500(0.80)^t`, where t represents the number of days since the population was first counted.

By comparing
`p(t)=500(0.80)^t` to (i) , we get

`A=500\text{ and } b=0.80`

i..e Initial population = 500

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