Answer:
see below
Step-by-step explanation:
1.
Adam's prediction can be modeled as:
P = 12500 x 1.02^n, where P is the population and n is the number of years.
When n = 7: P = 12500 x 1.02^7 = 14358.57085
Marcia's prediction can be modeled as:
P = 12500 + 600n, where P is the population and n is the number of years.
When n = 7: P = 12500 + 600 x 7 = 16700
Therefore, Marcia's model will result in a larger population 7 years from now as 16700 > 14358
2.
At n = 79
Adam's model predicts a population of: 59748.02887
Marcia's model predicts a population of: 59900
At n = 80
Adam's model predicts a population of: 60942.98945
Marcia's model predicts a population of: 60500
Up to year 79 Marcia's model predicts a higher population than Adam's model. However from year 80, Adam's model predicts a higher population that Marcia's.
(see attached graph for proof)
3.
Adam's model when n=50:
P = 12500 x 1.02^50 = 33644.85036
Marcia's model when n=50:
P = 12500 + 600 x 50 = 42500
Actual population when n=50: 35400
Difference between Adam's prediction and actual population:
35400 - 33644.85036 = 1755.149637
Difference between Marcia's prediction and actual population:
42500 - 35400 = 7100
Therefore, Adam's model gets closer to the actual population of 35400 as 1755.149637 < 7100
4. 35400 = 12500 + 50d, where d is the predicted growth each year
subtract 12500 from each side: 22900 = 50d
divide both sides by 50: 458 = d
Therefore, Marcia's new model assuming that the population will be 35,400 in 50 years is: P = 12500 + 458n
