IXL - Write exponential functions: word problems (Algebra 2 practice)

City Fitness, a popular gym, currently has 840 members. Based on its membership statistics since opening a few years ago, City Fitness expects to grow its membership by

each year.

Write an exponential equation in the form

(

)

that can model the number of members,

years.

Use whole numbers, decimals, or simplified fractions for the values of a and b.

ref_doc_title.

Learn with an example

question

Natalie is the creator of Better Brain, a new mindfulness app for teens. The app currently has 1,262 downloads, and Natalie has set a goal of doubling the downloads every month.

Write an exponential equation in the form

(

)

that can model Natalie's goal for the number of downloads,

months.

Use whole numbers, decimals, or simplified fractions for the values of a and b.

key idea

You can model a real-world situation involving an initial value and a constant growth or decay factor with an exponential equation in the form

(

)

where

and

≠

The constant

represents the initial value. It is the

-value

of the equation when

The constant

represents the growth or decay factor.

When the equation models exponential growth,
b
>
1
.
When the equation models exponential decay,
0
<
b
<
1
.

solution

An exponential equation in the form

(

)

can model Natalie's goal for the number of downloads,

months. To write the equation, first look for phrases in the problem that tell you about the initial value,

and the growth or decay factor,

Natalie is the creator of Better Brain, a new mindfulness app for teens. The app currently has 1,262

downloads,

and Natalie has set a goal of doubling the downloads every

month.

The constant

is the initial value. Natalie's app currently has 1,262 downloads. So,

1,262

The constant

is the growth factor, since Natalie expects the number of downloads to increase. Natalie's goal is to double the number of downloads each month, or that the number of downloads each month will be 2 times the number of downloads the month before. So,

The exponential equation

1,262

(

)

models Natalie's goal for the number of downloads.

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Teacher tools

Work it out

Not feeling ready yet? These can help:

Z.2Evaluate exponential functions

H.11Percent of change: word problems

V.7Write exponential functions from tables and graphs

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