Question

The population of two cities, City A and City B, in 1994 and 2004 were 1994 2004 City A 15,00019,000 City B 12,00017,500 Assume each continues to grow at a linear rate. (a) Write the equation of the population of City A. (Let x represent the number of years since 1994 and y represent the population of City A.) y

Answer 1

y = 400 x + 15,000

Explanation:

Let x represent the number of years since 1994 and y represent the population of City A.

When x = 0 (1994 - 1994), y = 15,000

When x = 10 (2004 - 1994), y = 19,000

The linear equation has the following form:

y = a . x + b

where,

a is the slope

b is the y-intercept

We can find the slope using the following expression.

a = Δy / Δx = 19,000 - 15,000 / 10 - 0 = 400

Then,

y = 400 x + b

To find b, we can replace the values of any of the points. Let's use the ordered-pair (0; 15,000).

15,000 = 400 . 0 + b

b = 15,000

The linear equation is

y = 400 x + 15,000