Citizen Math used to be called Mathalicious. If you have a current account on Mathalicious, you can use those credentials to log in to your Citizen Math account. Learn more here.  # I Remember

## How much should you trust your memory? How much should you trust your memory? According to neuroscientists, every time you remember something, you alter the memory a bit. The more you remember an event, the less accurate the memory becomes.

In this lesson, students use exponential decay to model memory fidelity and debate whether a bad memory is a good thing.

### REAL WORLD TAKEAWAYS

• Episodic memory does not work like a mental file cabinet from which we can retrieve perfect accounts of the past.
• Each time we remember an event we actually recreate and even alter it. Because the memory changes a little each time, the more times we remember an experience the less accurate it may become.

### MATH OBJECTIVES

• Write exponential decay equations given a description of a relationship
• Graph exponential decay functions
• (Optional) Use logs to solve an equation with a variable exponent

Appropriate most times as students are developing conceptual understanding. Algebra 1
Exponential Functions (Beg.) Algebra 1
Exponential Functions (Beg.)
Content Standards F.BF.1 Write a function that describes a relationship between two quantities. (a) Determine an explicit expression, a recursive process, or steps for calculation from a context. (b) Combine standard function types using arithmetic operations. For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model. (c) (+) Compose functions. For example, if T(y) is the temperature in the atmosphere as a function of height, and h(t) is the height of a weather balloon as a function of time, then T(h(t)) is the temperature at the location of the weather balloon as a function of time. F.BF.5 (+) Understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents. F.LE.1 Distinguish between situations that can be modeled with linear functions and with exponential functions. (a) Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals. (b) Recognize situations in which one quantity changes at a constant rate per unit interval relative to another. (c) Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another. F.LE.2 Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).
Mathematical Practices MP.2 Reason abstractly and quantitatively. MP.3 Construct viable arguments and critique the reasoning of others. MP.4 Model with mathematics. MP.7 Look for and make use of structure. MP.8 Look for and express regularity in repeated reasoning.