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?

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