Answered

IDNLearn.com makes it easy to get reliable answers from knowledgeable individuals. Discover in-depth and reliable answers to all your questions from our knowledgeable community members who are always ready to assist.

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 the 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.

Sagot :

The half life of the radioactive substance is 10.22 years.

What is Half Life ?

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

[tex]\rm y = 90 e^{-0.0678 * x}\\[/tex]

Half life is when the concentration is reduced to half

On 1st half life , the concentration = 90/2 = 45 mg

[tex]\rm 45 = 90 e^{-0.0678 * x}\\[/tex]

x = 10.22 years

Therefore the half life of the radioactive substance is 10.22 years.

To know more about Half Life

https://brainly.com/question/24710827

#SPJ1

Thank you for joining our conversation. Don't hesitate to return anytime to find answers to your questions. Let's continue sharing knowledge and experiences! Find the answers you need at IDNLearn.com. Thanks for stopping by, and come back soon for more valuable insights.