Answer:
x ≈ 5 years
Step-by-step explanation:
Given amount = A = 500 mg
Decay rate = r = 10% per year
Remaining amount = L = 295.25 mg
The formula to calculate remaining amount after x years decay =
L = A((100-r)/100)^x
By putting values in this formula, we get
295.25 = 500 ((100-10)/10)^x
295.25 = 500 (0.90)^x
295.25/500 = 0.90^x
0.5905 = 0.90^x
0.90^x =0.5905
taking log on both sides
ln(0.90^x) =ln(0.5905)
x*ln(0.90) =ln(0.5905) using property of log
x = ln(0.5905)/ln(0.90)
x = 4.9984
x ≈ 5 years
