Invent an Index An index is a number that describes an objec

Invent an Index

An index is a number that describes an object or process. For example miles per gallon is an index that describes how much gasoline is needed to drive a certain number of miles.

You are working for Consumer Reports and are given the task of identifying how well several popcorn machines pop popcorn.

Your boss, Mr. Spero, wants you to invent an index that quantifies how well each machine pops popcorn. The index should be:

larger index means a faster machine

all indices must be calculated with the same equation

Popcorn Machine A          Popcorn Machine B

Time [s]

Kernels Popped [k]

Time [s]

Kernels Popped [k]

12

6

20

10

18

9

30

15

24

12

50

25

Popcorn Machine C           Popcorn Machine D

Time [s]

Kernels Popped [k]

Time [s]

Kernels Popped [k]

6

6

6

5

12

12

12

9

20

20

24

17

1.Once you have an index for each machine write out the equation you invented to calculate it.

2.Think about the units of this index. How does this connect with graphing?

Solution

1) We choose the index: Kernels popped/Time taken.

For example. If 17 kernels are popped in 24 seconds, then the kernels popped per second=17/24=0.70833

2) The units of this index are [k][s]^-1

If we graph the kernels popped vs time taken, then the index represents the slope of this graph.