Question

The half-life of a certain radioactive material is 36 days. An initial amount of the material has a mass of 487 kg. Write an exponential function that models the

decay of this material. Find how much radioactive material remains after 5 days. Round your answer to the nearest thousandth.
Ο Α.
;0.318 kg
y = 487
B.
: 0.847
kg
y=
oc.
: 442.302 kg
y = 487
s(1
»=2(43);
OD
: 0 kg

Answer 1

• a(t) = 487(1/2)^(t/36)
• a(5) = 442.302 kg

Explanation:

The exponential function for half-life problems is easily written using 1/2 as the base of the exponent.

present value = (initial value) × (1/2)^(t/(half-life))

Then the amount (a) remaining after t days is ...

a(t) = 487 × (1/2)^(t/36)

__

After 5 days, the amount remaining is ...

a(5) = 487×(1/2)^(5/36) ≈ 442.302 kg

_____

Some folks like their exponential function to be written using e as the base for the exponent. Here, that would be ...

a(t) = 487·e^(-0.019254t)

where the constant in the exponent is -ln(2)/36.