x f(x)
0 32,000
1 29,440
2 27,048.80
3 ?
Sydney bought a new car for $32,000.00. If the car depreciates in value by 8% each year, the situation can be modeled by the equation f(x)=32,000(0.92)x . Complete the table to find the value of the car to the nearest cent after three years.(1 point) The value of the car after three years is $.
11 answers
To find the value of the car after three years, we can use the formula given:
\( f(x) = 32,000(0.92)^x \)
For \( x = 3 \):
\[ f(3) = 32,000(0.92)^3 \]
First, calculate \( (0.92)^3 \):
\[ 0.92^3 = 0.778688 \]
Now substitute this value back into the function:
\[ f(3) = 32,000 \times 0.778688 \]
Calculating the above:
\[ f(3) = 32,000 \times 0.778688 = 24,979.016 \]
To the nearest cent, the value of the car after three years is:
\[ \text{The value of the car after three years is } $24,979.02. \]
Let's go through the calculation again step by step.
We need to calculate the value of the car after 3 years using the formula:
\[ f(x) = 32,000(0.92)^x \]
For \( x = 3 \):
\[ f(3) = 32,000(0.92)^3 \]
First, we calculate \( (0.92)^3 \):
\[ 0.92^3 = 0.92 \times 0.92 \times 0.92 = 0.778688 \]
Now we substitute this back into the function:
\[ f(3) = 32,000 \times 0.778688 \]
Now, performing the multiplication:
\[ f(3) = 32,000 \times 0.778688 = 24,979.016 \]
Finally, rounding to the nearest cent:
\[ \text{Therefore, the value of the car after three years is } $24,979.02. \]
If my calculations contradict your expected answer, please let me know if there's any specific detail or different method you're expecting.
My apologies if there was any confusion in my previous responses regarding rounding and presentation. Let's calculate it again and ensure that we round correctly to the nearest cent.
Using the formula:
\[ f(x) = 32,000(0.92)^x \]
For \( x = 3 \):
First, we calculate \( (0.92)^3 \):
\[ 0.92^3 = 0.778688 \]
Next, we calculate \( f(3) \):
\[ f(3) = 32,000 \times 0.778688 \]
Calculating this gives:
\[ f(3) = 32,000 \times 0.778688 \approx 24,979.016 \]
Finally, rounding to the nearest cent:
\[ f(3) \approx 24,979.02 \]
So, the value of the car after three years, to the nearest cent, is:
\[ \text{The value of the car after three years is } $24,979.02. \]
If I misunderstood your question about rounding, please clarify what you need, and I'll be happy to assist further!
Cents in a dollar amount are represented in the two decimal places to the right of the dollar sign. For example:
Therefore, in the calculation we performed, when we calculated \( f(3) \) to be approximately 24,979.016, rounding to the nearest cent means we look at the third decimal place (the thousandths place). In this case:
This gives us:
So, the value of the car after three years, correctly formatted with cents, is \( \text{$24,979.02} \).
I apologize for any confusion in my previous responses. Let’s carefully go through the calculations one more time and ensure the final answer is accurate and correctly rounded to the nearest cent.
We'll start with the depreciation formula:
\[ f(x) = 32,000(0.92)^x \]
Now, for \( x = 3 \):
\[ f(3) = 32,000(0.92)^3 \]
Step 1: Calculate \( (0.92)^3 \)
\[ 0.92 \times 0.92 = 0.8464 \] \[ 0.8464 \times 0.92 \approx 0.778688 \]
Step 2: Calculate \( f(3) \)
Now, substitute \( (0.92)^3 \) back into the function:
\[ f(3) = 32,000 \times 0.778688 \]
Calculating that gives:
\[ f(3) = 32,000 \times 0.778688 \approx 24,979.016 \]
Step 3: Round to the nearest cent
The value \( 24,979.016 \) rounds to \( 24,979.02 \).
However, I recognize the possibility of error, so let's do it one more time with precise care:
Still rounding to cents, it will be \( 24,979.02 \), considering it is in the thousandths place (3rd decimal) where 6 should round up.
If it was previously noted that my answer was incorrect, please specify if there are earlier values to correct or confirm. Thank you for your patience as we clarify this detail!
Let’s go through the calculations step by step again, to clarify the confusion and ensure we get the correct value for the car after three years.
Using the formula for the depreciation:
\[ f(x) = 32,000(0.92)^x \]
For \( x = 3 \):
Calculate \( (0.92)^3 \): \[ (0.92)^3 = 0.92 \times 0.92 \times 0.92 \] Calculating it step by step:
Now plug it into the formula: \[ f(3) = 32,000 \times 0.778688 \] Performing the multiplication: \[ 32,000 \times 0.778688 \approx 24,979.016 \]
Rounding to the nearest cent:
If any bot provided \( 24,972.01 \), that suggests a possible calculation error or misunderstanding in the depreciation per calculation or in rounding.
The correct calculated value for the car's depreciation after three years, granted all calculations above are accurate, should indeed be:
\[ \text{The value of the car after three years is approximately } $24,979.02. \]
This implies that various aspects, including precision in calculations or methods, could lead to different outcomes, so I appreciate your patience while we clarify this. Let me know if there’s anything else I can assist you with!
