Mathematics: The half-life of a radioactive substance is the average amount of time it takes for half of its atoms to disentegrate. suppose you started with 200 grams of a substance with a half-life of 3 minutes. how may minutes have passed if 25 grams now remain? explain your reasoning.

If 12 is divided by 12 also then the answer will be 1....

The half-life of a radioactive substance is the

Ответ:

mariateamop

15.03.2022

Mathematics

To solve this, we are going to use the formula: $A=P( \frac{1}{2} ) ^{ \frac{t}{h} }$
where:

the final amount of the substance

is the initial amount of the substance

is the time

is the half life

We know from our problem that A=25

, and

. Lets replace those values in our formula:
$A=P( \frac{1}{2} ) ^{ \frac{t}{h} }$
$25=200( \frac{1}{2})^{ \frac{t}{3} }$

Notice that

is in the exponent, so we must use logarithms to bring it down:
$\frac{25}{200} =( \frac{1}{2} ) ^{ \frac{t}{3} }$
$ln( \frac{1}{2} )^{ \frac{t}{3} }=ln( \frac{25}{200} )$
$\frac{t}{3} ln( \frac{1}{2} )=ln( \frac{25}{250})$
$\frac{t}{3}= \frac{ln( \frac{25}{250} )}{ln( \frac{1}{2}) }$
$t= \frac{3ln( \frac{25}{250}) }{ln( \frac{1}{2}) }$
t=9

We can conclude that 9 minutes have passed after the substance started to decay for you to have 25 gr of the substance remaining.

0,0(0 оценок)

The half-life of a radioactive substance is the average amount of time it takes for half of its atoms to disentegrate. suppose you started with 200 grams of a substance with a half-life of 3 minutes. how may minutes have passed if 25 grams now remain? explain your reasoning.

Ответ:

Ответ:

Ask your question to the AI advisor

More tips

Answers on questions: Mathematics

Ask an AI advisor a question