Answer:
a) 
Now we can find the intercept using the first condition:


And the model would be given by:


The initial amount is A = 860 and we have:

Now we can use the second condition:

And solving for r we got:


And the model would be:

b) 
Step-by-step explanation:
Part a
For this case we have the following info given:

Where 0 represent the starting year in 1990.
And 5 years later we have 1210 people:

And we want to create a model like this:

And we can estimate the slope like this:
And replacing we got:

Now we can find the intercept using the first condition:


And the model would be given by:

And if we want an exponential model like this:

The initial amount is A = 860 and we have:

Now we can use the second condition:

And solving for r we got:


And the model would be:

Part b
For this case we want to estimate the population in the year 2000. And that represent 10 years from 1990 so then x =10 and replacing we got:

And for the exponential model we have:
