Answer:
y = 120·(23/12)^(x -8)
Explanation:
You want an exponential model that gives the two points (8, 120) and (9, 230).
Model
An exponential model can have the form ...
y = a·b^x
Ordinarily 'a' would represent the value of y when x=0, but we can translate the graph to the point (8, 120). The value of 'b' is the growth factor, the multiplier when the value of x increases by 1.
Here, the value of 'b' is 230/120 = 23/12, the multiplier as x increases by 1 from 8 to 9.
The function can be written with no rounding required as ...
y = 120·(23/12)^(x -8)
__
Additional comment
Some folks like to see an exponential function in the form ...
y = a·e^(kx)
In this form, a = 120·(23/12)^(-8) ≈ 0.659, and k = ln(23/12) ≈ 0.651, so the equation could be ...
y = 0.659·e^(0.651x)
The attachment shows the function we have written duplicates the given points more exactly. We like 4 or more significant figures in the constants involved in an exponential function, depending on how many significant figures are needed in the function values. 3 decimal places is not quite enough to properly give the ordered pair (9, 230).
<95141404393>