RUMM - Recursive and Exponential Models Lesson
Recursive and Exponential
Adapted from Course materials (IV.B Student Activity Sheet 3) for AMDM developed under the leadership of the Charles A. Dana Center, in collaboration with the Texas Association of Supervisors of Mathematics and with funding from Greater Texas Foundation.
5, 10, 20, 40, ...
This is an example of a geometric sequence. How do we generate the sequence in terms of the previous term? To find a value for each term, we must multiply the previous value by 2.
What information is required to find the value of the 10th term?
To find the value of the 10th term we need the values up to the 9th term.
What do you think the scatterplot of this sequence will look like?
Linear functions demonstrate constant addition, whereas exponential functions demonstrate constant multiplication. What is the constant ratio of the sequence? It is 2 because: 10/5 = 2 20/10=2 40/20=2
To find any term of a geometric sequence:
What is the 10th term of the sequence?
Since r=2, and we know the first term is 5 (a1), we can use the formula to the term value, n=10
Bouncing Balls
Different balls bounce at various heights depending on things like the type of ball, the pressure of air in the ball, and the surface on which it is bounced. The rebound percentage of a ball is found by determining the quotient of the rebound height (that is the height of each bounce) to the height of the ball before that bounce, converted to a percentage.
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