Question

the initial number of bacteria in a culture is 12,000. the xulture doubles each day write an exponential functin to model the population Y of bacteria after X days

Answer 1

The equation would be y=12000(2)ˣ.

This equation is of the form y=a*bˣ, where a is the initial population and b is the rate that it increases by. In this problem, a = 12000 and b=2, since it doubles each time.

Answer 2

`Y = 12,000 \cdot (2)^X`

Explanation:

The exponential function is given by:

`y =a \cdot b^x`

where,

a is the initial values and b is the growth factor.

As per the statement:

The initial number of bacteria in a culture is 12,000.

⇒Number of bacteria initially(a) = 12,000

It is also given that the culture doubles each day.

⇒ growth factor
`b= 2`

We have to find the exponential function to model the population Y of bacteria after X days.

By definition of exponential function:

`Y = 12,000 \cdot (2)^X`

where, x represents the days and Y is the population after X days.

Therefore, an exponential function to model the population is,

`Y = 12,000 \cdot (2)^X`