# Negative Rates

Warmup

Activity #1

Interpret Rate of Flow.

In this activity, you are going to investigate negative rate of change by observing a falling ladder. You have an incomplete question in the applet. Just pay attention to see when it is complete. Follow the instructions below.

• Click the play button, in the applet and watch the ladder as it goes down.
• Try to pause the play button when the question is complete. If you missed it, pull back the foot of the ladder until when it just appears.
• Now, answer the questions below.

(1.) How tall is the ladder?

(2.) How long did it take the top of the ladder to hit the ground?

(3.) What was the speed of the ladder when the question in the applet was complete?

(4.) Do you think the speed of the ladder was the same at any point during the fall?

(5.) Explain your reasoning.

Activity #2

Write an Equation to Model a Relation.

A student made a deposit of \$100 into his account. After every week, he withdraw \$20 to pay for transportation. Given that the account yielded no charges or interest, follow the instructions below to interact with the applet.

• Move the point on the line to see several instances in the account statement.

Activity #3

Solve Rate problem.

This section will give you the opportunity to apply your knowledge of negative rates.

• Read the following questions carefully before answering.

Describe a situation where each of the following quantities might be useful.

(1.) – 20 gallons per hour.

(2.) – 10 feet per minute.

(3.) – 0.1 kilograms per second

A submarine is only allowed to change its depth by rising toward the surface in 60-meter stages. It starts off at -340 meters.

(1.) At what depth is it after 1 stage?

(2.) At what depth is it after 2 stages?

(3.) At what depth is it after 4 stages?

(4.) How many stages will it take to return to the surface?

Challenge #1

A satellite recorded the movements of several boats. A motor boat traveled -3.4 miles per hour for 0.75 hours. How far did it go?

Challenge #2

From the previous problem, if a tugboat traveled -1.5 miles in 0.3 hours. What was its velocity?

Challenge #3

From the previous two problems, what do you think that negative distances and velocities could mean in this situation?

Quiz Time

https://www.ixl.com/math/grade-7/rate-of-change-graphs