Answer:
y = 2·5^x
Step-by-step explanation:
Using the given points, we can solve for 'a' and 'b'.
y = ab^x
2 = ab^0 = a . . . . . substitute (0, 2) for (x, y)
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1250 = 2·b^4 . . . . substitute for 'a' and (4, 1250) for (x, y)
625 = b^4 . . . . divide by 2
5 = b . . . . . . . take the 4th root
The function is ...
y = 2·5^x
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Additional comment
There are two real and two imaginary 4th roots of 625. Only the positive real root is useful as the base in an exponential function like this.
