The given equation is
[tex]V=23300(0.94)^t[/tex]
This equation represents the value of the car in dollars in t years after its purchase
Since the general form of the exponential equation is
[tex]Y=a(1\pm r)^t[/tex]
a is the initial value
r is the rate of increase (+) or decrease (-) in decimal
Compare the two equations
a = 23300
That means the purchase value of the car is $23300
Since the value in the bracket is less than 1, then use (1 - r)
1 - r = 0.94
To find r:
[tex]\begin{gathered} 1-r=0.94 \\ 1-0.94=r \\ 0.06=r \end{gathered}[/tex]
Then the rate is 0.06, change it to percent by multiplying it by 100%
[tex]\begin{gathered} r=0.06\times100\text{ \%} \\ r=6\text{ \%} \end{gathered}[/tex]
The answer is
The value of the care is V at the rate of 6%
The purchase price of the car was $23300
