Question

Twenty percent of a radioactive substance decays in ten years by what percent does the substance decay each year

Answer 1

Answer:

2%

Step-by-step explanation:

20% takes 10 years to decay

To find per year decay, we divide the percentage by the number of years, so we get unit rate of years {per year]. Thus we have:

20%/10 = 2% per year

It's that simple.

Hence, the percentage by which the substance decays each year is 2%

Answer 2

The substance decays $\boxed{2.2\% }$ each year if twenty percent of a radioactive substance decays in ten year.

Further explanation:

The exponential decay formula can be expressed as follows,

$\boxed{y = a{{\left( {1 - r} \right)}^x}}$

Here, $a$ represents the initial amount, $y$ is the final amount,$r$ is the rate of decay, and $x$ represents the time.

Given:

Twenty percent of a radioactive substance decays in ten year.

Explanation:

Consider the initial amount of the radioactive substance be $A.$

The final amount of the radioactive substance is $0.80A$

The rate of decay can be obtained as follows,

$\begin{aligned}0.80A &= A{\left( {1 - r} \right)^{10}}\\\frac{{0.80A}}{A} &= {\left( {1 - r} \right)^{10}}\\0.80 &= {\left( {1 - r} \right)^{10}}\\\sqrt[{10}]{{0.80}} &= 1 - r\\r&= 1 - \sqrt[{10}]{{0.80}}\\r&= 1 - 0.978\\r&= 0.022\\\end{aligned}$

The rate of decay is $2.2\%.$

The substance decays $\boxed{2.2\% }$ each year if twenty percent of a radioactive substance decays in ten year.

Learn more:

1. Learn more about inverse of the functionhttps://brainly.com/question/1632445.
2. Learn more about equation of circle brainly.com/question/1506955.
3. Learn more about range and domain of the function brainly.com/question/3412497

Answer details:

Grade: High School

Subject: Mathematics

Chapter: Exponential decay

Keywords: twenty percent, radioactive substance, decays, ten years, each year, rate of decay each year, substance.