Answer:
y = 5·4^x
Step-by-step explanation:
If you have two points, (x1, y1) and (x2, y2), whose relationship can be described by the exponential function ...
y = a·b^x
you can find the values of 'a' and 'b' as follows.
Substitute the given points:
y1 = a·b^(x1)
y2 = a·b^(x1)
Divide the second equation by the first:
y2/y1 = ((ab^(x2))/(ab^(x1)) = b^(x2 -x1)
Take the inverse power (root):
(y2/y1)^(1/(x2 -x1) = b
Use this value of 'b' to find 'a'. Here, we have solved the first equation for 'a'.
a = y1/(b^(x1))
In summary:
- b = (y2/y1)^(1/(x2 -x1))
- a = y1·b^(-x1)
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For the problem at hand, (x1, y1) = (2, 80) and (x2, y2) = (5, 5120).
b = (5120/80)^(1/(5-2)) = ∛64 = 4
a = 80·4^(-2) = 80/16 = 5
The exponential function is ...
y = 5·4^x
