A chemical compound decays at an exponential rate. The number of milligrams, y, of the compound left after hours is given by the
equation y = 250 • (3/5) t
, where t is the number of hours that have passed.
1. How much of the compound is left after 4 hours?
To find this, we simply substitute t = 4 into the equation:
y = 250 • (3/5)⁴
y ≈ 77.34 milligrams
Therefore, after 4 hours, approximately 77.34 milligrams of the compound are left.
2. How long does it take for the compound to decay to 125 milligrams?
To find this, we need to solve the equation for t when y = 125:
125 = 250 • (3/5) t
(3/5) t = 1/2
t = (log 1/2) / (log 3/5)
t ≈ 2.81 hours
Therefore, it takes approximately 2.81 hours for the compound to decay to 125 milligrams.