PLLLLZ I WILL GIVE BRAINIEST ANSWER AND 72 PTSA 500 mg known substance in fossils decays at a rate of 10% per year. Scientists find a fossil with 295.25 mg of the known substance. How old is the fossil?
Accepted Solution
A:
Answer:x ≈ 5 yearsStep-by-step explanation:Given amount = A = 500 mgDecay rate = r = 10% per yearRemaining amount = L = 295.25 mgThe formula to calculate remaining amount after x years decay =L = A((100-r)/100)^xBy putting values in this formula, we get295.25 = 500 ((100-10)/10)^x295.25 = 500 (0.90)^x 295.25/500 = 0.90^x0.5905 = 0.90^x0.90^x =0.5905taking log on both sidesln(0.90^x) =ln(0.5905)x*ln(0.90) =ln(0.5905) using property of logx = ln(0.5905)/ln(0.90)x = 4.9984x ≈ 5 years