IXL - Write exponential functions from tables and graphs (Algebra 1 practice)

This is the graph of an exponential function.

Write an equation for the function in the form

(

)

(

)

Use whole numbers, decimals, or simplified fractions for the values of

and

(

)

ref_doc_title.

Learn with an example

question

This is the graph of an exponential function.

Write an equation for the function in the form

(

)

(

)

Use whole numbers, decimals, or simplified fractions for the values of

and

(

)

key idea

The function

(

)

(

)

is an exponential

function,

where

and

are real numbers

(

≠

and

≠

The constant

is the function's initial

value.

It is the function's value when

The constant

is the function's growth or decay

factor.

When

the function models exponential growth. When

the function models exponential decay.

solution

You were asked to write an equation for the exponential function in the form

(

)

(

)

So, find the values of

and

First, find

It is equal to the function's value when

From the graph, you can see that

(

)

–

when

So,

–

To find

work out by what factor

(

)

gets multiplied when

increases by 1. For example, when

increases from 0 to 1, the graph tells you that

(

)

changes from

–

In other words,

(

)

gets multiplied by a factor of 4 when

increases from 0 to 1. That means that

Finally, use the values of

and

to write an equation for the function.

(

)

(

)

(

)

Substitute

–

and

–

(

)

Substitute

–

and

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