Questions: A company's product varies in cost depending on the number of features added to the standard features. The base cost is 10,000, and each additional feature adds 1,100 to the base cost. The company uses a cost function, C(n), to represent the cost of the product with n additional features. For example, C(1) represents the cost of 10,000 plus 1,100 for one additional feature. Which interpretation is accurate? C(5) is the base cost plus the cost of five additional features. C(3) is the base cost plus the cost of four additional features. C(1) is the base cost with just the standard features. C(4) is the base cost plus the cost of three additional features.

A company's product varies in cost depending on the number of features added to the standard features. The base cost is 10,000, and each additional feature adds 1,100 to the base cost. The company uses a cost function, C(n), to represent the cost of the product with n additional features. For example, C(1) represents the cost of 10,000 plus 1,100 for one additional feature.

Which interpretation is accurate?
C(5) is the base cost plus the cost of five additional features.
C(3) is the base cost plus the cost of four additional features.
C(1) is the base cost with just the standard features.
C(4) is the base cost plus the cost of three additional features.

Transcript text: A company's product varies in cost depending on the number of features added to the standard features. The base cost is $\$ 10,000$, and each additional feature adds $\$ 1,100$ tc the base cost. The company uses a cost function, $C(n)$, to represent the cost of the product with $n$ additional features. For example, $C(1)$ represents the cost of $\$ 10,000$ plus $\$ 1,100$ for one additional feature. Which interpretation is accurate? $C(5)$ is the base cost plus the cost of five additional features. $C(3)$ is the base cost plus the cost of four additional features. $\mathrm{C}(1)$ is the base cost with just the standard features. $\mathrm{C}(4)$ is the base cost plus the cost of three additional features.

Solution

Solution Steps

To solve this problem, we need to evaluate the cost function $ C(n) $ for different values of $ n $ and compare the results with the given interpretations. The cost function is defined as $ C(n) = 10000 + 1100 \times n $. We will calculate $ C(5) $, $ C(3) $, $ C(1) $, and $ C(4) $ to determine which interpretations are accurate.

Step 1: Calculate $ C(5) $

Using the cost function $ C(n) = 10000 + 1100n $, we find: \[ C(5) = 10000 + 1100 \times 5 = 10000 + 5500 = 15500 \]

Step 2: Calculate $ C(3) $

Next, we calculate: \[ C(3) = 10000 + 1100 \times 3 = 10000 + 3300 = 13300 \]

Step 3: Calculate $ C(1) $

Now, we compute: \[ C(1) = 10000 + 1100 \times 1 = 10000 + 1100 = 11100 \]

Step 4: Calculate $ C(4) $

Finally, we evaluate: \[ C(4) = 10000 + 1100 \times 4 = 10000 + 4400 = 14400 \]

Step 5: Interpret the Results

Now we compare the calculated values with the interpretations:

$ C(5) $ is the base cost plus the cost of five additional features: True (15500).
$ C(3) $ is the base cost plus the cost of four additional features: False (13300 is not equal to 10000 + 4400).
$ C(1) $ is the base cost with just the standard features: True (11100 is the base cost plus one feature).
$ C(4) $ is the base cost plus the cost of three additional features: False (14400 is not equal to 10000 + 3300).