The town of Pinedale, Wyoming, is experiencing a population boom. In 1990, the population was 860 and five years later it was 1210. (a) Find a linear model l(x) and an exponential model p(x) for the population of Pinedale in the year 1990+x. (b) What do these models estimate the population of Pinedale to be in the year 2000?

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:

both graphs increase on their domain

neither graph has a y-intercept

step-by-step explanation:

the following points can be visualized easily from the graph