Question

The number of hospitals in a certain country has been declining for many years. In 2014, there were 5,727 hospitals, but, in 2017, there were only 5,571. Assuming this trend is linear, write an equation for the number of hospitals H in the this country t years since 2000.
H=

Answer 1

Answer:

H = -52t + 6455

Step-by-step explanation:

2014 is 14 years since 2000. That gives you the point (14, 5727).

2017 is 17 years since 2000. That gives you the point (17, 5571).

Since we have two points in the line, we can find the equation of the line.

y = mx + b

m = slope = (difference in y)/(difference in x)

m = (5571 - 5727)/(17 - 14) = -156/3 = -52

y = -52x + b

Now we use one of the points for x and y, and we solve for b.

5727 = -52(14) + b

b = 6455

The equation is

y = -52x + 6455

Using H and t, we have

H = -52t + 6455