IXL - Exponential functions over unit intervals (Algebra 1 practice)

How does

(

)

change over the interval from

(

)

decreases by 5%

(

)

increases by 5%

(

)

increases by 400%

(

)

decreases by a factor of 5

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Learn with an example

question

How does

(

)

change over the interval from

(

)

increases by 9

(

)

decreases by 9

(

)

decreases by a factor of 9

(

)

increases by 800%

solution

To see how a function changes over an interval, look at the endpoints.

The values of

(

)

at the endpoints

and

are:

(

)

(

)

In the values

and

the same base is raised to different exponents. So, to see how

(

)

changes from

you should find the ratio of these two values.

(

)

(

)

Divide by subtracting the exponents

–

Divide by subtracting the exponents

This means

(

)

(

)

So,

(

)

increases by a factor of 9 over the interval from

You can also describe this change using percentages. A value increases by

if it changes by a factor of

100

Rewrite the factor 9 in

(

)

(

)

so it has this form.

(

)

(

)

(

)

(

)

800

100

(

)

(

)

800

100

(

)

(

)

800

(

)

This means

(

)

is 800% larger than

(

)

So,

(

)

increases by 800% over the interval from

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Work it out

Not feeling ready yet? These can help:

V.1Evaluate an exponential function

R.5Division rule for exponents

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