math question

[porterehd]

An element with mass 670 grams decays by 27.3% per minute. How much of the element is remaining after 9 minutes, to the nearest 10th of a gram?

i need to know How much of the element is remaining after 9 minutes,

An element with mass 670 grams decays by 27.3% per minute. How much of the element is remaining after 9 minutes, to the nearest 10th of a gram i need the answer to the nearest 10th

 

[Deleted member 4993]

An element with mass 670 grams decays by 27.3% per minute. How much of the element is remaining after 9 minutes, to the nearest 10th of a gram?

i need to know How much of the element is remaining after 9 minutes,

What have you learned about exponential decay function?

Please show us what you have tried and exactly where you are stuck.

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[Dr.Peterson]

An element with mass 670 grams decays by 27.3% per minute. How much of the element is remaining after 9 minutes, to the nearest 10th of a gram i need the answer to the nearest 10th

One way to do this would be to find the amount remaining after the first minute (that is, 27.3% less than the starting amount, 670 g), then repeat to find the amount remaining after the second minute, and so on. That might reveal a pattern, if you know nothing about the topic.

Or, maybe you have learned a formula for "exponential decay". Unfortunately, there are several ways to state such a formula, and because you did not follow the rules by showing some work or telling us what you've learned, we can't tell which form you learned.

Once you tell us what formula you learned, if any, and where you are stuck in applying it, we will be able to help you.

 

[HallsofIvy]

You start with 679 grams and it decays by 27,3% per minute,

Okay, in the first minute it decays by 0.273(679)= 185.367 g. Do you understand what the means? It "decays" by that amount means that it loses 185.367 g mass so, after one minute, has mass 679- 185.367= 484.633 g.

In the second minute it decays by 0.273(484.633)= 132.304809 so after the second minute has mass 484.633- 132.304809= 352.328191.

Now what happens during the third minute, the fourth, etc up to the ninth minute? You might want to choose a decimal place to round to rather than get more and more decimal places.

(There is a simpler way to do this proglem but this method follows directly from the definitions.)

 

[Deleted member 4993]

An element with mass 670 grams decays by 27.3% per minute. How much of the element is remaining after 9 minutes, to the nearest 10th of a gram?

i need to know How much of the element is remaining after 9 minutes,

An element with mass 670 grams decays by 27.3% per minute. How much of the element is remaining after 9 minutes, to the nearest 10th of a gram i need the answer to the nearest 10th

The method of solving this problem would be similar to that shown to you in:

math 1

A new car is purchased for 17000 dollars. The value of the car depreciates at 13.5% per year. What will the value of the car be, to the nearest cent, after 12 years?

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Did you finish that problem?

 

[HallsofIvy]

An element with mass 670 grams decays by 27.3% per minute. How much of the element is remaining after 9 minutes, to the nearest 10th of a gram?

i need to know How much of the element is remaining after 9 minutes,

An element with mass 670 grams decays by 27.3% per minute. How much of the element is remaining after 9 minutes, to the nearest 10th of a gram i need the answer to the nearest 10th

There were initially 670 grams. Since it decays by 27.3% per minute, there is left (100- 27.3)%= 72.7% per minute. That means that after one minute there is 72.7% of 670= 0.727(670)= 487.09 grams left. And after the second minute there is 72.7% of 487.09= 0.727(487.09)= 354.11443 grams left. And after the third minute there is 72.7% of 354.11443= 0.727(354.11443)= 257.44119061 grams left. Can you continue that for nine minutes?

A simpler way- notice that we are just repeatedly multiplying by 0.727:
\(\displaystyle 487.09= 0.727(670)\)
\(\displaystyle 354.11443= 0.727(487.09)= 0.727(0.727(670))= 0.727^2(670)\)
\(\displaystyle 257.44119061= 0.727(354.11443)= 0.727(0.727^2(670))=0.727^3(670)\)

You might find it simpler to calculate \(\displaystyle 0.727^9(670)\).