To determine the initial value of Rhonda's car at the moment she bought it, we need to consider the given depreciation function [tex]\( C(t) = 25,000 \cdot (0.751)^t \)[/tex].
This function describes how the value of the car decreases over time, where:
- [tex]\( C(t) \)[/tex] is the value of the car at time [tex]\( t \)[/tex]
- [tex]\( 25,000 \)[/tex] is the coefficient which represents the initial value of the car
- [tex]\( 0.751 \)[/tex] is the depreciation factor per unit of time [tex]\( t \)[/tex]
- [tex]\( t \)[/tex] is the time elapsed
The initial value of the car is given by the function when [tex]\( t = 0 \)[/tex]:
[tex]\[
C(0) = 25,000 \cdot (0.751)^0
\][/tex]
Any number raised to the power of zero is 1, so:
[tex]\[
C(0) = 25,000 \cdot 1 = 25,000
\][/tex]
Therefore, the initial value of Rhonda's car at the moment she bought it is \[tex]$25,000.
The correct answer is:
\[
\$[/tex] 25,000
\]
