Question

2, Find the value of the van 8 years after its purchase, Show your reasoning. 3, In the same year (2008), the business bought a second van that cost $10,000 less than the first van and depreciates at 10% per year, Would the second van be worth more or less than the first van 8 years after the purchase? Explain or show your reasoning, 4. On the same coordinate plane as the graph you chose in the first question, sketch a graph that shows the value of the second van. in dollars, as a function of years since its purchase.

Answer 1

Explanation:

1. To find the value of the first van 8 years after its purchase, we need to consider its depreciation rate. If we assume a depreciation rate of 15% per year, we can calculate the value of the van using the formula:

Value of van after 8 years = Purchase price * (1 - Depreciation rate)^Number of years

Let's say the purchase price of the first van is $20,000. Plugging in the values, we have:

Value of van after 8 years = $20,000 * (1 - 0.15)^8

= $20,000 * (0.85)^8

Calculating this, we find that the value of the first van 8 years after its purchase is approximately $6,978.

2. Now let's consider the second van. We know that it cost $10,000 less than the first van and depreciates at a rate of 10% per year. To find its value 8 years after its purchase, we can use the same formula as before:

Value of second van after 8 years = (Purchase price of first van - $10,000) * (1 - Depreciation rate)^Number of years

Using the values, we have:

Value of second van after 8 years = ($20,000 - $10,000) * (1 - 0.10)^8

= $10,000 * (0.90)^8

Calculating this, we find that the value of the second van 8 years after its purchase is approximately $4,782.

3. Comparing the values, we can see that the first van is worth more ($6,978) than the second van ($4,782) after 8 years. This is because the second van depreciates at a higher rate (10% per year) compared to the first van (15% per year). The higher depreciation rate causes the second van's value to decrease at a faster rate over time.

4. To sketch a graph that shows the value of the second van in dollars as a function of years since its purchase, we can plot the number of years on the x-axis and the value of the van on the y-axis. We can use the formula mentioned earlier:

Value of second van = ($20,000 - $10,000) * (1 - 0.10)^Number of years

We can choose a few values for the number of years (e.g., 0, 2, 4, 6, 8) and calculate the corresponding values of the van. Then, we can plot these points on the graph and connect them to get a curve that represents the decreasing value of the second van over time.