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A biologist has a 2952 -gram sample of a radioactive substance. Find the mass of the sample after five hours if it decreases according to a continuous exponential decay model, at a relative rate of 13% per hour.
Do not round any intermediate computations, and round your answer to the nearest tenth.

Sagot :

Raphealnwobiidn

The mass of the radioactive sample after 5 hours is 1471g

An exponential function is the form:

y = abˣ

where y, x are variables, a is the initial value of y and b is the multiplier.

Let y represent the mass of sample remaining after x hours.

Given an initial 2952g sample, hence a = 2952.

Also, there is a decay of 13% per hour, hence:

b = 100% - 13% = 87% = 0.87

The equation becomes:

y = 2952(0.87)ˣ

After 5 hours:

y = 2952(0.87)⁵

y = 1471g

The mass of the radioactive sample after 5 hours is 1471g

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