Question

Select the correct answer from each drop-down menu.

A camp director developed the function m(c) = 12c + 80 to model the total cost of taking c campers on a field trip to the movies.


In the camp director’s function, the number of campers is the _______ variable and the total cost of the trip _________


1. ( independent, dependent )

2. ( changes by a constant factor per camper, Changes by a constant amount per camper )

.

Answer 1

dependent, changes by a constant factor per camper.

Explanation:

Answer 2

(a) Independent variable

(b) The constant factor is 12

Explanation:

Given

`m(c) = 12c + 80`

c = campers

m = total cost

Solving (a) What type of variable is the number of campers (c)

The total cost (m) is dependent on the number of campers (c) for its own value.

In other words, if c changes from 5 to say 7, the value of m will also change.

This implies that the number of campers is an Independent variable

Solving (b): Constant factor

This in other words means, rate of change (or slope)

A linear function is:

`y = ax + b`

Where a represents the slope

By comparison with:
`m(c) = 12c + 80`

Hence, the constant factor is 12