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
The relationship between the number of hospitals and the years, is a linear function.
The equation for the number of hospitals is: [tex]H = -52t + 6455[/tex]
Let
[tex]t \to[/tex] years since 2000
[tex]H \to[/tex] number of hospitals since 2000
So, we have:
[tex](t_1,H_1) = (14,5727)[/tex] ---- 2014
[tex](t_2,H_2) = (17,5571)[/tex]
Calculate the slope (m)
[tex]m = \frac{H_2 - H_1}{t_2 - t_1}[/tex]
This gives:
[tex]m = \frac{5571 - 5727}{17-14}[/tex]
[tex]m = \frac{-156}{3}[/tex]
[tex]m = -52[/tex]
The linear equation is then calculated using:
[tex]H = m(t - t_1) + H_1[/tex]
So, we have:
[tex]H = -52(t - 14) + 5727[/tex]
[tex]H = -52t + 728 + 5727[/tex]
[tex]H = -52t + 6455[/tex]
Hence, the equation H is: [tex]H = -52t + 6455[/tex]
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