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