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

Question

asked Mar 11, 2018 124k views

1 Answer

Jney · Answer 1 · 2018-03-17T23:40:36+0000

Answer:

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.