7.1.4 What if it does not grow?

Exponential Decay

StandardsA‑CED.1. Create equations in one variable

and use them to solve problems.F‑IF.8b. Use the properties of exponents to

interpret expressions for exponential functions. For example, identify percent rate of change in functions such as y = (1.02)t, y = (0.97)t, y = (1.01)12t, y = (1.2)t/10, and classify them as representing exponential growth or decay.

F‑IF.7e. Graph exponential functions, showing intercepts and end behavior.

More StandardsF‑LE.1c. Recognize situations in which a

quantity grows or decays by a constant percent rate per unit interval relative to another.

F‑LE.2. Construct exponential functions given a graph, a description of a relation‑ship, or two input‑output pairs (include reading these from a table).

F‑LE.5. Interpret the parameters in a linear or exponential function in terms of a context.

The M & M LabStart with a cup full of M & Ms.Trial #1: Dump the M & Ms out on your team’s

workspace. Remove any candies that are “M” down. Record the number of candies that remain in a table as shown on a slide that follows.

Trial #2: Gather the candies that show an “M”. Put these candies back in the cup, shake them up, and dump them on your workspace again. Remove any candies that are “M” down and count the number of candies that remain. Record the number in your table.

Trial #x: Continue this process until the last candy is removed. Record all results in your table.

The M & M Lab cont.Make a scatterplot of the data

collected in your table.Once perfected, graph your team

results on the class graph on the smart board.

Questions Prior to LabWhat does trial #0

represent?

Is it possible that a team conducting this experiment might never remove their last candy? Explain.

The M & M Lab DataTrial Number (x) Number of

Candies Remaining (y)

0

1

2

3

4

Questions After LabWhere does the graph cross the y-

axis?Does the graph have any

asymptotes?Is this situation increasing or

decreasing?Using your knowledge about the

probability of flipping a coin, what would you expect or estimate the generator (multiplier) to be?

Write an equation to model the data.Could there be a value for ?Does this lab model an arithmetic or

geometric sequence? How do you know?

Exit TicketMrs. Pierce’s sons built a 100 pound

snowman. In the warm weather, half of the snowman melts away every day. Write an equation that models the weight of the snowman (y) after x days.