ALEX Classroom Resources

   View Standards     Standard(s): [MA2019] PRE-19 (9-12) 1 :

1. Define the constant ein a variety of contexts.

Example: the total interest earned if a 100% annual rate is continuously compounded.

a. Explore the behavior of the function y=e^x and its applications.

b. Explore the behavior of ln(x), the logarithmic function with base e, and its applications.

In this lesson, students will:

• write an exponential function that represents the amount of water in a tank after t seconds if the height of the water doubles every 10 seconds.
• discover Euler’s number e by numerically approaching the constant for which the height of water in a tank equals the rate of change of the height of the water in the tank.
• calculate the average rate of change of a function.