Question

From 1990 to 1996, the population of Oregon increased by about 60,300 people per year. In 1996, the population was about 3,024,000. Write a linear model for the population P of Oregon from 1990 to 1996. Let t represent the number of years since 1990. Then use your model to estimate the population of Oregon in 2014. You may use a calculator on this problem.

a. P(t) = 60,300t + 3,024,000; P(24) = ?
b. P(t) = 60,300t - 3,024,000; P(24) = ?
c. P(t) = 60,300t + 3,024,000; P(24) ≈ 5,922,600
d. P(t) = 60,300t - 3,024,000; P(24) ≈ 1,584,000

Answer 1

The linear model for Oregon's population from 1990 to 1996 is P(t) = 60,300t + 3,024,000. The population in 2014, 24 years after 1990, is estimated to be approximately 4,471,200.

Step-by-step explanation:

The question pertains to writing a linear model for the population of Oregon from 1990 to 1996 and using it to estimate the population in 2014. Since the population increased by about 60,300 people each year and the population was 3,024,000 in 1996, the linear model can be represented as P(t) = 60,300t + 3,024,000, where t represents the number of years since 1990. To estimate the population of Oregon in 2014, which is 24 years since 1990, we substitute t with 24 in the model:

P(24) = 60,300(24) + 3,024,000 = 1,447,200 + 3,024,000 = 4,471,200.

Thus, the correct statement for the estimated population of Oregon in 2014 is approximately 4,471,200.