Sequences that increase at increasing rates are sometimes described as “growing exponentially”. However, this is not always a correct use of the word. For example, both quadratic (constant second difference) and exponential growth share this property.

Question

Suppose that a sequence begins 1, 2, 4. . .
a. What are the first ten terms of the sequence if it grows exponentially? b. What are the first ten terms of the sequence if it grows quadratically?
c. Compute the ratio of the 10th terms of the two sequences

Answer 1

The sequences are

1,2,4,8,16,32,64,128,256,512,1024
1,2,4,9,16,25,36,49,64,81,100

1024/100 = 256/25 = (16/5)^2