Answer:
a) 
b) 
Step-by-step explanation:
For this case we have the following info:
represent the initial amount of bacteria
represent the population of bacteria after 6 hours
Part a
For this case we use the proportional model given by:

Where P represent the population at time t and k is a constant of proportionality.
We can rewrite the model like this:

And if we integrate both sides we got:

Now if we apply exponential we got:


For this case using the initial condition:

We have the following model:

Using the second condition
we have this:

We can divide both sides by 660 and we got:

Now we can apply natural log on both sides and we got:


So then the model would be given by:

Part b
For this case we just need to replace t=3 into the model and we got:
