An element with mass 820 grams decays by 26.8% per minute. how much of the element is remaining after 18 minutes, to the nearest 10th of a gram?

3.0 grams of the element are left after 18 minutes

Step-by-step explanation:

Recall that an exponential decay that can be studied with the following formula for the amount of material (A) as a function of time (t):

where:

is the starting amount of the substance (in our case 820 grams)

r is the rate of decay (which in our case given as 26.8% can be written in decimal form as 0.268

and t is the time in minutes (in our case t = 18 minutes)

Then we have:

which can be rounded to 3.0 grams

=====================================

explanation

the graph has a slope of 1/3 because each time you move up 1, you go to the right 3. so, slope = rise/run = 1/3. we can cross choice a off the list since we want a slope of 3, rather than 1/3.

the first table shown has a slope of -3. this is because the rise is -6 and the run is 2, so slope = rise/run = -6/2 = -3. note how x increases by 2 each time (run) and y drops by 6 each time (rise). choice b can be eliminated.

the second table has a slope of 3. each time x goes up by 1, the y values increase by 3. slope = rise/run = 3/1 = 3. alternatively you can use the slope formula to prove that the slope is 3 here. use any two rows of values to generate the two points. choice c is one of the answers

the third table also has a slope of 3. let's use the slope formula to prove as such. i'm going to use the first two rows of the table. so i'll use the two points (2,1) and (5,10)

m = slope

m = (y2-y1)/(x2-x1)

m = (10-1)/(5-2)

m = 9/3

m = 3 so we get a slope of 3

choice d is the other answer

answer:

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payment for service including tax

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explanation:

service only with 20% tip  

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in the opening of the question the word 'service' is associated only with the pretax value.

the closing part of the question asks: how much did she pay for the  

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so technically the answer is  

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$

72.6

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however, the intention of the question provider may have been that your answer is to be  

$

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$

94.09

to 2 decimal places.

'

payment just for service  

→

$

87.12

payment for service including tax

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$

94.09

tony b

mar 21, 2017

answer:

trying to explain it another way

explanation:

service charge  

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$

72.60

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20

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add

$

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8

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