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A radioactive substance disintegrates at a rate proportional to the mass present at any instant. If the disintegration rate is $0.023 /$ year, what percent of the original sample remains at the end of 10 years?

$$79.45 \%$$

Algebra

Chapter 4

Exponential and Logarithmic Functions

Section 7

Applications of Exponential and Logarithmic Functions

McMaster University

Harvey Mudd College

Idaho State University

Lectures

01:17

Twenty percent of a radioa…

09:17

Assume that the rate at wh…

01:33

Radioactive Decay What per…

02:30

A radioactive element deca…

04:57

Suppose the half-life of a…

01:46

Radioactive Decay Radioact…

01:31

The rate of decomposition …

03:17

Finding the Rate If the ha…

given disintegration rate of 0.23 per year. What percent of this particular substance would be remaining after 10 years? So let's start by calculating the half life of this substance. So the half life is going to be equal to the natural log of two Divided by that disintegration rate 0.023. It gives us a half life which is equal to about 30.1 36 years Now let's go ahead and we're going to be using the second formula for this first formula here. But we need to first calculate the number of half lives that have surpassed. So this is after 10 years Which means end is going to be equal to those 10 years divided by the half life of 30.13, 6 years. That gives us end which is equal to 0.3318. So only about a third of a half life has passed after these 10 years. Now we can go ahead and plug in these values to that first formula. So it's this ending amount that we're trying to find. I'm just going to refer to that as a we started with Now it didn't give us this actual start amount in terms of mass, but we're looking for this percent remains. Let's just call it 100% that we started with started with 100% of whatever substance this is Divided by two to the power of energy. Just found to be 0.3318, Calculate that. So 100 divided by two to the power of 0.3318 gives us this ending percent equal to 79.5%.

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