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 mg b. 12 mg c. 40 mg d. 194 mg

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,

Where,

is the amount at any time t,

is the original amount,

n=72 is the half-life

t=365 number of days

Substituting all the values,

Approximately 4.84=5 mg

Therefore, Option A is correct.  

After 396 days, there will only be 5 mg of Terbium-160.                        

is there any attachment? what are the equations?

x = central angle apc = measure of minor arc ac

the two angles x and 30 add to 180, so x+30 = 180 and x = 180-30 = 150. the measure of minor arc ac is 150 degrees.

what we need to do from here is find the circumference and then multiply it by x/360 since there are 360 degrees in a circle. in this case, x = 150, so x/360 = 150/360 = 15/36 = 5/12. the shortest distance along the curve from a to c is 5/12 of the distance around the entire circle (aka circumference)

c = circumference

c = pi*d

c = pi*24

c = 24pi

now multiply this by 5/12 to get

distance along minor arc ac = (5/12)*(circumference)

distance along minor arc ac = (5/12)*(24pi)

distance along minor arc ac = 10pi

the formula you can use is

l = (x/360)*pi*d

with

l = length of minor arc

x = central angle

d = diameter

which essentially is the steps we took though a bit differently.