A tire swing attached to a tree branch swings with an arc length of 30 feet on its first swing. On each swing following the first, the tire's arc length is 6/7of the length of the previous swing. Let an represent the arc length on the nth swing.
A) Find a formula that describes an. Express the common ratio as a fraction. Hint: Use an = a1r^n-1 and place r in parentheses!
an = ________________
B) What is the arc length of the tire on the 11th swing? Round your answer to three decimal places.
________________ feet
C) How many swings does it take before the arc length is less than one foot? Round your answer to a whole number. Hint: You must use the strategy for solving an exponential equation!
_________________
