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At noon a radioactive sample decays at a rate of 4,000 counts per minute. at 12:30 pm, the decay rate has decreased to 2,000 counts per minute. the reduced decay rate at 1:30 pm, is

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sqdancefan
The decay rate is cut in half each half-hour, so after 1 more hour it will be 1/2*1/2 = 1/4 of the rate at 12:30.

The reduced decay rate at 1:30 pm is 500 counts per minute.
MrRoyal

The reduced decay rate at 1:30 pm, is 0.25

How to determine the reduced decay rate?

The initial rate at noon is:

Initial = 4000

At 12:30 pm

New = 2000

The above means that the decay rate from noon to 12:30 is:

Rate = (4000 - 2000)/4000

Rate = 0.5

This means that the decay rate per 30 minutes is 0.5

There are 2 30 minutes from 12:30 pm to 1:30 pm.

So, the reduced decay rate at this time is:

Rate = 0.5^2

Evaluate

Rate = 0.25

Hence, the reduced decay rate at 1:30 pm, is 0.25

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