Try It
Have you ever had a special secret that you shared with a friend, and suddenly everyone knew your secret? If so, you may have been surprised at how quickly your secret spread around. One friend tells another friend, and then those friends tell more friends, and suddenly, your secret is not so secret.
The pattern of spreading the secret around can be modeled algebraically.
Use your knowledge of arithmetic sequences as linear functions and geometric sequences as exponential functions to complete the activity below.
Tip
The nth term of an arithmetic sequence with the first term a sub 1 and the common difference d is given by a sub n equals a sub 1 plus the quantity n minus one times d, where n is a positive integer. This can be simplified and translated into the slope-intercept form of a linear equation y equals m times x plus b. The nth term of a geometric sequence with the first term a sub 1 and the common ratio r is given by a sub n equals a sub 1 times r to the power of n minus 1. This can be simplified and translated into an exponential equation y equals a times b to the power of x.
