MATH SOLVE

2 months ago

Q:
# A population of bacteria begins with 1 bacterium and triples every hour. Which equation can be used to model this situation?A. y = 3xB. y = 3x^2C. y = x^3D. y = 3^x

Accepted Solution

A:

Answer:The correct option is D.Step-by-step explanation:It is given that the population of bacteria begins with 1 bacterium and triples every hour. Let initial population be 1.[tex]P(0)=1[/tex]The population of bacteria after 1 hour is[tex]P(1)=1\times 3=3^1=3[/tex]The population of bacteria after 2 hour is[tex]P(2)=3\times 3=3^2=9\[/tex]Similarly the population of bacteria after n hour is[tex]P(n)=3\times 3\times ...\times 3=3^n[/tex]If x is number of hours and y is the population of bacteria after x hour, then[tex]y=3^x[/tex]The other way to find the population model is shown below.The population model is defined as[tex]P=a(1+b)^x[/tex]Where, a is initial population and (1+b) is growth factor.In the given situation the initial population is 1 and growth factor is 3, therefore[tex]y=3^x[/tex]Therefore option D is correct.