Cambridge International Mathematics

InChapter 22we were given data for two related variablesxandy, and we used technology to find aline

of best fit y=ax+b to connect the variables.

This process is calledlinear regression.

We will now use technology to connect variablesxandyby anexponential modelof the formy=a£bx.

For example, consider the table of values: t^25812

H 40 113 320 1280

We can performexponential regressionon this data using aTI-84 Plus.

Instructions for doing this can be found on page 28.

For this data we find that H¼ 20 : 0 £(1:414)t.

Notice that thecoefficient of determination r^2 =1, which indicates that

the data follows an exponential curve exactly.

To test whether two variablesxandyare related by an exponential model of the form y=a£bx,we

should do the following:

² Graphyagainstx. The graph

should look like either or

² Perform exponential regression using a graphics calculator. The closerr^2 is to 1 , the better the

exponential model fits the data.

Example 9 Self Tutor

Time,tdays 1 2 3 4 5

Weight,Wgrams 11 20 35 62 118

a Use technology to show that an exponential model fits the data well.

b Find the exponential model.

c Use the model to estimate the original weight of the culture.

a Putting the data into lists and using exponential regression we get:

As r^2 ¼ 1 , an exponential model fits the data very well.

b W¼ 6 : 09 £ 1 : 80 tgrams

c When t=0, W¼ 6 : 09 £ 1 : 80 o

¼ 6 : 09

So, the original weight was about 6 : 09 grams.

E EXPONENTIAL MODELLING [3.2]

EXPONENTIAL

The does not perform exponential REGRESSION

regression in this form, but you can click on the icon to

access an alternative exponential regression program.

Casio fx-9860G

O

y

x O

y

x

EXPONENTIAL

REGRESSION

The weight grams of bacteria

in a culture was measured

regularly. The results were:

W

576 Exponential functions and equations (Chapter 28)

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