Respuesta :
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.
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:
[tex]Y = 12,000 \cdot (2)^X[/tex]
Step-by-step explanation:
The exponential function is given by:
[tex]y =a \cdot b^x[/tex]
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 [tex]b= 2[/tex]
We have to find the exponential function to model the population Y of bacteria after X days.
By definition of exponential function:
[tex]Y = 12,000 \cdot (2)^X[/tex]
where, x represents the days and Y is the population after X days.
Therefore, an exponential function to model the population is,
[tex]Y = 12,000 \cdot (2)^X[/tex]
