Handout 06
Chapter 05
Fall 2014
Math 018
Name: _____________________
Directions: Read each question carefully and answer as clearly as possible. When completed, place in your binder.
Rainbow trout (Oncorhynchus mykiss) taken from four different localities along the Spokane River during July,
August, and October of 1999 were analyzed for heavy metals by the Washing State Department of Ecology. As
part of this study, the length (in millimeters) and weight (in grams) of each trout were measured. The table below
shows a subset of this data.
a.
The scatterplot below uses Length as the x-variable and Weight as the y-variable. Comment on the
shape of the data. Is it more linear or exponential in shape? Can you find a “best fit” exponential
equation? Why is this more difficult than finding the “best fit” linear?
Length (mm)
Weight (g)
150
202
180
209
240
223
280
310
320
350
324
353
337
363
347
432
351
506
365
540
Answer:
Length vs Weight (Raidbow Trout)
600
500
Weight (grams)
400
300
200
100
0
0
50
100
150
200
Length (mm)
250
300
350
400
b.
The scatterplot below uses length as the x-variable and Log(weight) as the y-variable. Comment on
the shape of the data. Is it more linear or exponential in shape? Use a straight edge to sketch in a
line of “best fit” and find the equation of the line.
Length
Weight
Log(Weight)
150
202
2.305
180
209
2.320
240
223
2.348
280
310
2.491
320
350
2.554
324
353
2.548
337
363
2.560
347
432
2.635
351
506
2.704
365
540
2.732
Answer:
Length vs Log(Weight) (Rainbow Trout)
2.8
2.75
Log(Weight) (log(grams))
2.7
2.65
2.6
2.55
2.5
2.45
2.4
2.35
2.3
2.25
0
50
100
150
200
Length (mm)
250
300
350
400
c.
Notice that the linear equation from part (b) has Log(weight) as the y-variable or output and length as
the x-variable or input. That is, we found an equation of the form:
Log(weight)  m  length  b
Use algebra and properties of logarithms to manipulate the above equation so that it looks like the
exponential equation weight  y0Mlength . Then, determine formulas for the growth multiplier and yintercept of the exponential equation based off of the slope and y-intercept of the transformed linear
equation.
Let x = length
Let y = weight
Answer: