An exponential function of form f(x) = b^x includes the points (2, 16), (3, 64), and (4, 256). What is the value of b?
The value of b is __.
(Type a whole number.)
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An exponential function of form f(x) = b^x includes the points (2, 16), (3, 64), and (4, 256). What is the value of b?
The value of b is __.
(Type a whole number.)
To determine the value of ( b ) in the exponential function ( f(x) = b^x ), we can use the given points.
1. From the point ( (2, 16) ):
[
f(2) = b^2 = 16
]
This implies:
[
b^2 = 16 implies b = 4 quad (text{since } b text{ must be positive})
]
2. Let’s check this value with the other points:
– For ( (3, 64) ):
[
f(3) = b^3 = 4^3 = 64 quad text{(Correct)}
]
– For ( (4, 256) ):
[
f(4) = b^4 = 4^4 = 256 quad text{(Correct)}
]
Since the calculations are consistent, the value of ( b ) is:
[
boxed{4}
]