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:

dc=6 square root of 3 and ac is 12 square root 3

c and d

step-by-step explanation:

square root of 3/2 = 18/c

cross multiply to get 18*2=√3*c

36/√3 * √3/√3 = c

c= 36*√3/3

c=12√3

i think its a and d

step-by-step explanation: