7th Grade Math

Lesson 1B Rates and Functions 379

Functions are often written as equations with two variables—one

to represent the input and one to represent the output. Here’s an

equation for the situation in Example 1.

=

Function rule: multiply by 20

Input: number of months Output: total savings

ANIMALS An armadillo sleeps 19 hours each day. Write an

equation using two variables to show the relationship between

the number of hours h an armadillo sleeps in d days.

Input Function Rule Output

Number of

Days (d)

Multiply

by 19

Number of

Hours Slept (h)

11 × 19 19

22 × 19 38

33 × 19 57

dd × 19 19 d

Words

Variable

Equation

Number of equals number times 19 hours

hours slept of days each day.

Let d represent the number of days.

Let h represent the number of hours.

h = 19 d

How many hours does an armadillo sleep in 4 days?

h = 19 d Write the equation.

h = 19 ( 4 ) Replace d with 4.

h = 76 Multiply.

An armadillo sleeps 76 hours in 4 days.

BOTANIST A botanist discovers that a certain species of bamboo

grows 4 inches each hour.

b. Write an equation using two variables to show the relationship

between the growth g in inches of this bamboo plant in h hours.

c. Use your equation to explain how to find the growth in inches

of this species of bamboo after 6 hours. Then solve.

Input and Output

When x and y are used

in an equation, x usually

represents the input,

and y usually represents

the output.

Real-World Link

Armadillos have the

ability to remain

underwater for as

long as six minutes.

Because of the

density of its armor,

an armadillo will sink

in water unless it

inflates its stomach

with air, which often

doubles its size.

RR

A

377_384_C07_L1_895130.indd 379 12/31/09 4:23 PM