To fill in the missing value for [tex]\( f(x) \)[/tex] at [tex]\( x = 0 \)[/tex] in the given table, we need to evaluate the exponential function [tex]\( f(x) = (1.01)^x \)[/tex] at [tex]\( x = 0 \)[/tex].
Step-by-Step Solution:
1. Start with the exponential function:
[tex]\[
f(x) = (1.01)^x
\][/tex]
2. Substitute [tex]\( x = 0 \)[/tex] into the function:
[tex]\[
f(0) = (1.01)^0
\][/tex]
3. Any number raised to the power of 0 is 1:
[tex]\[
(1.01)^0 = 1
\][/tex]
Therefore, the value of [tex]\( f(0) \)[/tex] is 1.
Given the choices:
a. 0
b. 1.01
c. 1.001
d. 1
The correct choice is:
D
