Question

(100 POINTS) The cost per guest for an all-inclusive day trip of no more than 100 people is modeled by the function c(x) = 400 + 2x. The number of guests is modeled by the function g(x) = 100 − x, where x represents the number of guests fewer than 100 that register for the trip. Evaluate( c∙g)(18)

(please round the total cost for the trip to the nearest dollar)

Answer 1

Explanation:

To evaluate (c ∙ g)(18), we need to substitute the value of 18 into both functions and then multiply the results.

First, let's evaluate c(x) = 400 + 2x with x = 18:

c(18) = 400 + 2(18)

c(18) = 400 + 36

c(18) = 436

Next, let's evaluate g(x) = 100 - x with x = 18:

g(18) = 100 - 18

g(18) = 82

Now, let's multiply c(18) and g(18):

(c ∙ g)(18) = c(18) * g(18)

(c ∙ g)(18) = 436 * 82

(c ∙ g)(18) = 35,752

Therefore, the total cost for the trip, rounded to the nearest dollar $35,752

Answer 2

$35,752

Explanation:

The total cost of the trip is calculated by multiplying the cost per guest by the number of guests.

So, the equation for the total cost is:

`\sf (c\cdot g)(x) = c(x) * g(x)`

To evaluate (c∙g)(18), we need to first find the values of c(18) and g(18).

`\sf c(18) = 400 + 2(18) = 400+36= 436`

`\sf g(18) = 100 - 18 = 82`

Now, we can multiply c(18) and g(18) to find the total cost of the trip:

`\begin{aligned} (c\cdot g)(18) & = c(18) \cdot g(18) \\\\ &= 436 \cdot 82 \\\\ & = 35,752 \end{aligned}`

Therefore, the total cost of the trip is $35,752.