The question is an illustration of an exponential function
The cost of treatment when d = 1 is $273
How to determine the cost of treatment
From the graph, we have the following ordered pairs
(x,y) = (0,150) and (0.5,202.5)
The graph represents an exponential function:
[tex]y = ab^x[/tex]
When (x,y) = (0,150), the equation becomes
[tex]150 = ab^0[/tex]
[tex]a=150[/tex]
When (x,y) = (0.5,202.5), the equation becomes
[tex]202.5 = ab^{0.5}[/tex]
Substitute 150 for a
[tex]202.5 = 150b^{0.5}[/tex]
Divide both sides by 150
[tex]1.35 = b^{0.5}[/tex]
Square both sides
[tex]b = 1.82[/tex]
So, the equation of the graph is:
[tex]y = 150 * 1.82^x[/tex]
When x = 1, we have:
[tex]y = 150 * 1.82^1[/tex]
[tex]y = 273[/tex]
Hence, the cost of treatment when d = 1 is $273
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