Rate of change for a banquet hall question

[lealr1984]

Two banquet halls are being considered for a wedding reception. Hall A charges $40.00 per person, and Hall B charges $2,000.00 + $25.00 person. The graph of the banquet hall costs is shown below.



A) What is the rate of change for each banquet hall(including units)?

B) Identify the approximate point at which both halls cost the same amount. Describe the conditions under which one hall would be cheaper than the other. Include references to the initial conditions of the graph and the rate of change of the graph.

Does this have to be solved only by a graphing calculator?

 

[stapel]

Two banquet halls are being considered for a wedding reception. Hall A charges $40.00 per person, and Hall B charges $2,000.00 + $25.00 person. The graph of the banquet hall costs is shown below.

View attachment 4774

A) What is the rate of change for each banquet hall(including units)?

Use what you learned back in algebra: Convert the English statements into linear models for each hall. Then look at the slopes. What is their meaning in this context?

B) Identify the approximate point at which both halls cost the same amount.

"Approximate" means "from the pretty picture" (rather than "exact", which of course you can find from the algebra). So look at the picture they gave you, and copy down a number.

Describe the conditions under which one hall would be cheaper than the other.

Since the y-value is the cost, then the relative heights of the lines tell you which hall is more expensive and which is less, for any given x-value number of people. So look at the pretty picture, and think about what the x- and y-values mean.

Does this have to be solved only by a graphing calculator?

No. Heck, you don't even need calculus! :wink:

 

[Steven G]

Math problems should never be solved using a calculator unless the numbers are just ridulous -like 214*316

 

[Steven G]

Both equations are LINES according to the diagram. Do you know what a derivative is, NOT how to compute a derivative but what a derivative is?!
The rate of change of a line is simply the slope of the line

Part B: You are being asked to find the point of intersection of two lines.

The reason why Calculus students get low grades is NOT because Calculus is hard. In fact, the Calculus part of Calculus is actually quite easy. The trouble students have is the Calculus DEMANDS that you know your algebra very well and many students do not have a solid algebra background.

Jomo