Problema Solution
The swing in Marty’s backyard slows down exponentially after his little sister jumps off. If it’s swinging 3 feet
back and forth when she jumps off, and the size of the motion decays at a steady rate of 5% per second, how
long before the swing is only moving back and forth 1 inch?
Answer provided by our tutors
let
y = the swinging distance back and forth
x = the time
y = a*b^x
where a and b are constants
for x = 0 s we have y = 3 ft
3 = a*b^0
a = 3
for x = 1 s the size of the motion decays by 5% that is y = 3 - 0.05*3 = 0.95*3
0.95*3 = 3*b
b = 0.95
the exponential equation that describes the swinging is
y = 3*(0.95)^x
we need to find x such that y = 1 in
1 = 3*(0.95)^x
3*(0.95)^x = 1 divide both sides by 3
(0.95)^x = 1/3
x = 21.42 s
click here to see the step by step solution of the equation
after 21.42 seconds the sing is only moving back and froth 1 inch.