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

Initial population = 500

Decay factor of population =0.80

Step-by-step explanation:

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

...(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 , where t represents the number of days since the population was first counted.

By comparing to (i) , we get

i..e Initial population = 500

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

< coa = 150 ( given)

as ba and bc are tangents

so oc and oa is perpendicular to cb and ab respectively because in circle normal passes through centre

so in quadrilateral oabc

< coa + < oab + < ocb + < abc = 360

150 +90+90 + < abc = 360

330 + < abc = 360

< abc = 360 -330 = 30

so < abc = 30

⭐dhruv⭐

the function makes a strait line horizontally with no x intercept but a y intercept at 9.