Task Sets: Recognize constant rate situations - Common Core Math - HS Functions

Concepts

Complete the definition: "A constant rate of change means the same [BLANK] is
added (or subtracted) for each unit increase in the independent variable."

BLANK:

Which phrase signals that a situation involves a constant rate of change?

"The population triples every decade."

"The account balance grows by 4% each month."

"A worker earns $18 for every hour worked."

"The value increases by a factor of 1.2 each year."

A student sees this description: "A savings account earns 3% interest each year."
The student classifies it as a constant rate situation and writes $f(t) = 0.03t + b$ .
What error did the student make?

The student used the wrong variable name.

The student confused constant percent rate (exponential) with constant rate (linear).

The student forgot to include the initial value $b$ .

The student should have written $f(t) = 3t + b$ instead.

Procedures

A plumber charges a $60 service fee plus $45 per hour. Which function correctly
models the total cost $C$ (in dollars) for $h$ hours of work?

$C(h) = 45h$

$C(h) = 60h + 45$

$C(h) = 45h + 60$

$C(h) = 105h$

A 750-gallon tank drains at a constant rate of 6 gallons per minute. Write the
linear function $V(t) = mt + b$ that gives the volume remaining after $t$ minutes.
What is the slope $m$ ?

A 750-gallon tank drains at a constant rate of 6 gallons per minute. Using the
function $V(t) = mt + b$ for the volume remaining after $t$ minutes, what is
the y-intercept $b$ ?

A phone plan charges $35 per month with no activation fee. Using the function
$C(m) = 35m + b$ , what is the value of $b$ ?

A car rental company charges a $40 flat deposit plus $0.25 per mile driven.
The function is $C(d) = 0.25d + 40$ . What does the value $0.25$ represent in context?

The total cost when no miles are driven.

The cost per mile driven.

The flat deposit charged at pickup.

The maximum number of miles allowed.

HSF.LE.A.1.b Tutor Intake — Recognizing Constant Rate Situations

Concepts

Procedures