Question

Finn bought a yoyo from a company that claims that, with each retraction, the string rolls up by 80% of the original length. He sets up a tape measure and throws the yoyo 3 times. His data are charted below.
Throw Length of string (feet)
1 3
2 2.4
3 1.92
Finn wants to find the sum of the length of string after 10 throws. What is the sum of the lengths, rounded to the nearest hundredth?

Answer 1

1st      3                       0.80                  2.40                    
2nd     2.40                  0.80                  1.92                    
3rd     1.92                  0.80                  1.54                    
4th     1.54                  0.80                  1.23                    
5th     1.23                  0.80                  0.98                    
6th     0.98                  0.80                  0.79                    
7th     0.79                  0.80                  0.63                    
8th     0.63                  0.80                  0.50                    
9th     0.50                  0.80                  0.40                    
10th   0.40                  0.80                  0.32
total:  13.39

13.39 rounded to 13.40 is the sum of the length of string after 10 throws.

Based on the table: I generated the formula:

f(x) = 3 × 0.80ˣ

where the exponent x represents the number of throws.