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

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answer:

at time x=0 we have 1000, at time x=1 we have 2000, at time x=2 we have 4000.  

so that's an initial value of 1000 and a ratio of 2,

y = 1000 (2^x)

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