How are the functions f (x) = 16 Superscript x and g (x) = 16 Superscript one-half x related?
1.The output values of g(x) are one-half the output values of f(x) for the same value of x.
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2.The output values of g(x) are one-quarter the output values of f(x) for the same value of x.
3.The output values of g(x) are the square root of the output values of f(x) for the same value of x.
4.The output values of g(x) are the square of the output values of f(x) for the same value of x.
Answers
Answer:
In the previous examples, we were given an exponential function, which we then evaluated for a given input. Sometimes we are given information about an exponential function without knowing the function explicitly. We must use the information to first write the form of the function, then determine the constants a and b, and evaluate the function.
HOW TO: GIVEN TWO DATA POINTS, WRITE AN EXPONENTIAL MODEL.
If one of the data points has the form
(
0
,
a
)
, then a is the initial value. Using a, substitute the second point into the equation
f
(
x
)
=
a
(
b
)
x
, and solve for b.
If neither of the data points have the form
(
0
,
a
)
, substitute both points into two equations with the form
f
(
x
)
=
a
(
b
)
x
. Solve the resulting system of two equations in two unknowns to find a and b.
Using the a and b found in the steps above, write the exponential function in the form
f
(
x
)
=
a
(
b
)
x
.