Question

9375 grams of radioactive material decays every hour in a geometric fashion. After 4 hours of decay, 15 grams of radioactive material remains. Assuming the decay continues at the same rate, determine the exact amount of radioactive material that would remain by the 7th hour of decay.

Answer 1

The amount of radioactive material that would remain by the 7th hour of decay is 0.12 grams.

Exponential function

An exponential function is in the form:

y = abˣ

where y,x are variables, a is the initial value and b is the multiplicative factor.

Let y represent the amount of substance remaining after x hours. Hence:

a = 9375, at x = 4, y = 15:

15 = 9375(b)⁴

b = 0.2

y = 9375(0.2)ˣ

For the 7th hour, x = 7:

y = 9375(0.2)⁷ = 0.12

The amount of radioactive material that would remain by the 7th hour of decay is 0.12 grams.

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