The half-life of radium-226 is about 1,590 years. How much of a 100mg sample will be left in 500 years? Write your answer rounded to the nearest tenth.

There will be left 80.4 of the sample in 500 years

Step-by-step explanation:

Radioactive Decay Model

Suppose N is the size of a population of radioactive atoms at a given time t, No is the size of an initial population of radioactive atoms at time t = 0, and k is the decay constant, then the equation is as follows:

The time required for half of the original population of radioactive atoms to decay is called the half-life Th. The relationship between the half-life and the decay constant is:

We know the half-life of radium-226 is about 1,590 years. We can find the value of k by solving the above equation:

k=0.000436

The initial mass of the sample is 100 gr, thus the model for the mass at time t is:

When t=500 years:

M(500)=80.4 gr

There will be left 80.4 of the sample in 500 years

x = -5

step-by-step explanation:

step-by-step explanation:

points a and b are equidistant from the desired line, so the line you find by using them will go through point r.

using points other than a and b will give the desired line only if they are equidistant from r. if they are randomly located, the perpendicular line you create will not necessarily go through point r, hence will not be a solution to the problem.