[MOVED] 100 students if $250 fees; 6 fewer for each $20 incr  TOPIC_SOLVED

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[MOVED] 100 students if $250 fees; 6 fewer for each $20 incr

Postby Tooter on Mon Mar 16, 2009 3:19 pm

Here is a word problem I am having difficulty solving:

"The director of a summer camp estimates that 100 students will enroll if the tuition is $250. For each $20 increase in tuition, six fewer students will enroll.
a. Determine a linear function that will predict the number of students who will enroll at a given tuition.
b. use this model to predict erollment when the tuition is $300.

I think this is looking for something like: f(x)= -----
Where do I go from here?
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Postby stapel_eliz on Mon Mar 16, 2009 5:26 pm

Tooter wrote:I think this is looking for something like: f(x)= -----

Yes, they've told you to find a function, and your function will start with "(function name) equals".

Tooter wrote:"The director of a summer camp estimates that 100 students will enroll if the tuition is $250. For each $20 increase in tuition, six fewer students will enroll.
a. Determine a linear function that will predict the number of students who will enroll at a given tuition.

They've given you one point; namely, (x, y) = (250, 100).

They've given you information sufficient to find the "next" point; namely, (270, 94).

They've told you to find the linear model for these two points.

Find the slope of the line through these points. Then pick one of the points (it doesn't matter which) and plug it, along with the slope you just found, into point-slope formula for a straight line.

Solve this equation for "y=". Rename "y" as "f(x)", to restate the formula as a function.

Tooter wrote:b. use this model to predict erollment when the tuition is $300.

Plug "300" in for "x", and evaluate to find the required value.

If you get stuck, please reply showing how far you have gotten in following the step-by-step instructions.

Thank you! :D
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