Asked by Sara V.
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.
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
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
Answers
Answered by
Steve
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
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
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