A radioactive substance decays from 90 mg to 12.6 mg in 29 years according to the exponential decay model y=ae−bx , where a is t

Question

2 years ago

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A radioactive substance decays from 90 mg to 12.6 mg in 29 years according to the exponential decay model y=ae−bx , where a is t

he initial amount and y is the amount remaining after x years.
Find the b -value.

Use the EXACT b -value to write the exponential decay model for this substance with initial amount 90 mg, then use that model to find the half-life.

Find the half-life.

Mathematics

1 answer:

MrMuchimi · Answer 1 · 2023-08-28T08:56:43+03:00

The half life of the radioactive substance is 10.22 years.

Half Life is the amount of time needed by the radioactive substance to reduce to its half concentration (as compared to the initial concentration).

It is given that

y = ae⁻ᵇˣ

here a is the initial amount , y is the amount remaining after x years

a = 90mg at x =0

Value of y = 12.6 mg at x = 29 years

On substitution of value

12.6 = 90 e⁻²⁹ᵇ

0.14 = e⁻²⁹ᵇ

b = 0.0678

The equation is

$\rm y = 90 e^{-0.0678 * x}\\$