Question

A population of bacteria begins with 1 bacterium and triples every hour. Which equation can be used to model this situation?

A. y = 3x

B. y = 3x^2

C. y = x^3

D. y = 3^x

Answer 1

The correct option is D.

Explanation:

It is given that the population of bacteria begins with 1 bacterium and triples every hour.

Let initial population be 1.

`P(0)=1`

The population of bacteria after 1 hour is

`P(1)=1* 3=3^1=3`

The population of bacteria after 2 hour is

`P(2)=3* 3=3^2=9\`

Similarly the population of bacteria after n hour is

`P(n)=3* 3* ...* 3=3^n`

If x is number of hours and y is the population of bacteria after x hour, then

`y=3^x`

The other way to find the population model is shown below.

The population model is defined as

`P=a(1+b)^x`

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

`y=3^x`

Therefore option D is correct.