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the number of bacteria in a container increases at the rate of R(t) bacteria per hour. If there are 1000 bacteria at time t=0 , which of the following expressions gives the number of bacteria in the container at time t=3 hours?

Respuesta :

CastleRook
The number of bacteria will modeled using exponential growth function, this is given by:
f(x)=a(b)^x
where
a is the initial amount
b=ratio of growth
x=time
Thus from our information we shall have:
f(x)=R(t)
a=1000
b=r
t=x
hence we shall model the situation by:
R(x)=1000(r)^t
Hence in 3 years time the population will be modeled by the function:
R(x)=1000(r)^3=1000r³

The number of bacteria in the container at time t=3hours will be[tex] R(x)=1000r^{3}[/tex]

Given  the number of bacteria initially is a= 1000 ,and initial time is t=0 and growth ratio b=r  and also it is given f(x)=R(t)

How to solve expression using exponential growth function?

To solve the expression we will model the expression using exponential growth funtion as

 [tex]f(x)=a(b)^{x}[/tex] where ,

a = initial amount

b = ratio of growth

x = time  

Now, we will model the situation as [tex]R(x)=1000r^{t}[/tex]

Therefore,it will be modeled by the function [tex]R(x)=1000r^{3}[/tex] in 3 years ie.t=3

Learn more about exponential growth function here: https://brainly.com/question/9917816