Question

According to your model, as the population of San Francisco was revitalizing, for what value of the independent variable t did it reach 750 thousand

Answer 1

Answer:

  t =1.453 decades from 1980 i.e in year 1994.5

Step-by-step explanation:

Given:

- Population @ year 1980 P = 678.97 thousands.

- Population @ year 2000 P = 776.73 thousands.

- The rate of increase is linear - constant rate.

Find:

As the population of San Francisco was revitalizing, for what value of the independent variable t did it reach 750 thousand ?

Solution:

- Develop an expression of population P as a function of time t in decades elapsed from year 1980 on-wards

- The linear expression can take a form of :

                                      P(t) = m*t + C

- Where, m is the rate of increase.

              C is the initial population.

- Formulate m:

                                       m = (776.73 - 678.97) / 2 = 48.88

- Formulate C:

                                       C = P (@ 1980) = 678.97

- Evaluate P(t) = 750:

                                       P(t) = 48.8*t + 678.97

                                       750 = 48.8*t + 678.97

                                       t = 71.03/48.8

                                      t =1.453 decades