IXL - Write exponential functions: word problems (Algebra 1 practice)

Heather just got hired as an administrative assistant at Haven Enterprises. Her starting salary is

45,500

and her contract ensures that she will get a 3% salary increase each year.

Write an exponential equation in the form

(

)

that can model Heather's salary,

after

years.

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

ref_doc_title.

Learn with an example

question

A scientist is developing a new method to reduce the population of a certain invasive insect species. For an experiment, the scientist starts with 2,500 insects. She predicts that her new method will reduce the number of insects in the experiment by 14% each week.

Write an exponential equation in the form

(

)

that can model the predicted number of insects,

in the experiment after x weeks.

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

y =

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 the predicted number of insects,

in the experiment after x weeks. To write the equation, first look for phrases in the problem that tell you about the initial value,

and the growth or decay factor,

A scientist is developing a new method to reduce the population of a certain invasive insect species. For an experiment, the scientist starts with 2,500

insects.

She predicts that her new method will reduce the number of insects in the experiment by 14% each

week.

The constant a is the initial value. The scientist starts her experiment with 2,500 insects. So,

2,500

The constant b is the decay factor, since the number of insects will decrease. The rate of decrease is 14% each week, or 0.14. In other words, the number of insects each week will be

–

0.14

0.86

times the number of insects the week before. So,

0.86

The exponential equation

2,500

(

0.86

)

models the predicted number of insects.

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Teacher tools

Work it out

Not feeling ready yet? These can help:

V.1Evaluate an exponential function

H.11Percent of change: word problems

V.7Write exponential functions from tables and graphs

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