Terbium-160 has a half-life of about 72 days. After 396 days, about how many milligrams of a 220 mg sample will remain?A. 5 mgB. 12 mgC. 40 mgD. 194 mg
Accepted Solution
A:
Answer:Option A = 5 mg Step-by-step explanation:Given : Terbium-160 has a half-life of about 72 days.To find : After 396 days, about how many milligrams of a 220 mg sample will remain?Solution :We have given the Terbium-160 has a half-life of about 72 days. We can represent the situation with an exponential function,[tex]A_t = A_0(0.5)^{\frac{t}{n}}[/tex]Where,[tex]A_t[/tex] is the amount at any time t,[tex]A_0=220[/tex] is the original amount,n=72 is the half-lifet=365 number of daysSubstituting all the values,[tex]A_t =220(0.5)^{\frac{396}{72}}[/tex][tex]A_t =220(0.5)^{5.5}[/tex][tex]A_t =220(0.022)[/tex][tex]A_t =4.84[/tex]Approximately 4.84=5 mgTherefore, Option A is correct. After 396 days, there will only be 5 mg of Terbium-160.