Exercises: Recognize Constant Rate Situations

Which statement correctly describes the slope of a linear function?

A table of values for a function is shown. Which conclusion is correct?

A function has the rule $f(x) = 4x + 7$. What is the rate of change (slope)?

Which phrase signals a constant rate of change (linear situation)?

A phone company charges $0.05 per text message. Which statement about this situation is correct?

A 400-gallon water tank drains at 5 gallons per minute. Write the linear function $V(t)$ for the volume (in gallons) remaining after $t$ minutes.

Enter your answer in the form $V(t) = \_\_t + \_\_$ (e.g., write the slope first, then the y-intercept separated by a space, like "-5 400").

Which of the following describes a constant RATE situation (not a constant percent rate)?

A plumber charges a flat service fee of $80 plus $60 per hour. Write the linear function $C(h)$ for total cost (in dollars) as a function of hours $h$ worked.

Enter your answer in the form "slope intercept" (e.g., "60 80" for $C(h) = 60h + 80$).

A gardener plants 8 seeds per row. After planting $r$ rows, the total seeds planted is $S(r) = 8r$. What is the rate and initial value?

A swimming pool holds 15,000 gallons and is being drained at 200 gallons per hour.

The rate of change is   ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲   gallons per hour (negative means decreasing).
The initial value is   ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲   gallons.
The function is $V(t) =$   ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲   $t +$   ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲   .

Which situation is a constant PERCENT rate, not a constant rate?

A ball is dropped and falls $16t^2$ feet in $t$ seconds. A student says this is a constant rate situation because distance changes "per second." Is the student correct?

A monthly phone plan costs $40 per month with no activation fee. Which function and interpretation are BOTH correct?

A candle starts at 24 cm tall and burns at 1.5 cm per hour.

After how many hours will the candle be completely burned out? (When $V(t) = 0$.)

A city's population grows by exactly 2,000 people per year.

A demographer wants to use a linear model for the next 50 years. Explain one reason the constant rate assumption might be reasonable and one reason it might break down over a 50-year period.

What error did the student make?

What error did the student make?

A store charges $5 per item for the first 10 items, then $3 per item for any items beyond 10. Write a piecewise linear function $C(n)$ for the total cost of $n$ items, and explain why each piece has a constant rate.

A linear model predicts that a city of 50,000 people grows by 1,500 residents per year. After 30 years, the model predicts a population of 95,000.

(a) State the function $P(t)$.
(b) Explain two factors that could make this model unreasonable over a 30-year period, and describe what type of model might better capture the long-term behavior.