Brief Calculus.

Question

The population of a small town has shown a linear increase in the years from 1990 to 1995. In

the year 1990 the population was 2,125 people. In the year 1995 the population was 2,500 people.

a) Write a linear function relating the population of the town as a function of the year.

b) What is the slope? Write a sentence interpreting the meaning of the slope in this scenario.

Answer 1

If this is linear, then the two points of that linear functions are:

(0, 2125) and (5, 2500)

To get the slope:

m = (2500 - 2125)/ (5-0) = 75

Where 1990 is the starting year (t=0), and 1995 is five years later (t=5).

(a) Using the point slope form:

y - 2125 = 75( t - 0)

y = 75t + 2125

Therefore the population P as a function of time (t) is:

P(t) = 75t + 2125

where t is the number of years and t=0 means year 1990.

(b)The slope is m=75. This means that the population is constantly increasing at a rate of 75 per year.