Answer:
y = 0.4·5^x
Explanation:
You want an exponential function y = a·b^x that passes through the points (1, 2) and (3, 50).
Setup
The given point values give two equations in two unknowns when used in the given exponential form:
y = a·b^x
2 = a·b^1
50 = a·b^3
Solution
Dividing the second equation by the first, we find b:
50/2 = (ab^3)/(ab)
25 = b^2 . . . . . simplify
5 = b . . . . . . . . . square root
Then the value of 'a' can be found from the first equation:
2 = a·5
a = 2/5 = 0.4
Exponential function
Using these values of 'a' and 'b', we have the exponential function ...
y = 0.4·5^x
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Additional comment
The exponential regression function of your calculator can tell you the same thing.