To determine which functions correctly represent the value of Jeffrey's car after it depreciates by 5% per year, let's evaluate each one:
1. [tex]\( V(t) = 17,000 (1 + 0.05)^t \)[/tex]
- This equation implies that the value of the car is increasing by 5% each year. Since we know the car is depreciating, this does not represent the correct situation.
- Therefore, the answer is:
[tex]\[
\square No
\][/tex]
2. [tex]\( V(t) = 17,000 (1 - 0.05)^t \)[/tex]
- This equation correctly represents the value of the car as depreciating by 5% each year. The factor [tex]\((1 - 0.05)\)[/tex] or 0.95 correctly models a 5% annual decrease.
- Therefore, the answer is:
[tex]\[
\square Yes
\][/tex]
3. [tex]\( V(t) = 17,000 (0.95)^t \)[/tex]
- This is another correct representation of the depreciation process. The value 0.95 within the equation directly indicates a yearly reduction by 5%.
- Therefore, the answer is:
[tex]\[
\square Yes
\][/tex]
4. [tex]\( V(t) = 17,000 (1.05)^t \)[/tex]
- This equation implies the value of the car is increasing by 5% annually, which is contrary to our information that the value depreciates.
- Therefore, the answer is:
[tex]\[
\square No
\][/tex]
In summary, the functions that correctly represent the depreciation of Jeffrey's car are:
[tex]\[
V(t) = 17,000 (1 - 0.05)^t \quad \text{and} \quad V(t) = 17,000 (0.95)^t
\][/tex]
