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Identify the y-intercept (initial value) in the function

f(x)=130.27)^x
a .27
b. 3.51
c. 13
d .27

User Colonder
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1 Answer

3 votes

Final answer:

The y-intercept of the function (130.27)^x is found by evaluating the function at x=0. Since any number to the power of 0 is 1, the y-intercept is 1, which does not match the provided options. If the function has a typo and should be 130(0.27)^x, then the y-intercept would be 130 assuming x=0.

Step-by-step explanation:

To identify the y-intercept (initial value) in the function f(x) = (130.27)^x, we need to evaluate the function when x is zero, since the y-intercept is the value of the function when it crosses the y-axis. Mathematically, this means finding f(0).

Putting x=0 into the function, we get f(0) = (130.27)^0. Any non-zero number raised to the power of 0 equals 1. Therefore, f(0) = 1, which tells us the y-intercept of the function. However, none of the provided options a. 27 b. 3.51 c. 13 d. 27 match this value, so there might have been a misunderstanding in the question or a mistake in the presentation of options.

If we assume the function was intended to be f(x) = 130(0.27)^x, then for x=0, we get f(0) = 130(0.27)^0 = 130(1) = 130, and the y-intercept of the function would be 130. This matches with answer choice c. 13 if we allow for a decimal point typo, changing it to 130.

User Bekliev
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