100 were students interviewed, 28 took PE, 31 took bio, 42 took English, 9 took PE and biology, 10 took PE and english, 4 took a
ll three subjects.
(1) how many students took none of the three subjects.
(2) how many students took PE, but not biology or English.
(3) how many students took biology and PE but no English. 
(1) how many students took none of the three subjects.
(2) how many students took PE, but not biology or English.
(3) how many students took biology and PE but no English.
1 answer:
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$50.00 after 0 months and $37.50 after 6 months.
We first must calculate half-life using the attached formula.
Half-Life = (time * ln(2)) / ln (beginning amount/ending amount)
Half-Life = (6 * 0.69314718056) / ln (50.00 / 37.50)
Half-Life = ( <span> <span> <span> 4.1588830834 </span> </span> </span> ) / ln ( <span> <span> <span> 1.3333333333 </span> </span> </span> )
Half-Life = ( <span> <span> 4.1588830834 </span> </span> ) / 0.28768207245
Half-Life = <span> <span> <span> 14.456525038 </span> </span> </span> months
Now we need to calculate "lambda"
lambda = ln(2) / half-life
lambda = 0.69314718056 / <span>14.456525038
lambda = </span><span><span><span>0.0479470121 </span> </span> </span>
Next we have to use this formula:
Ending Amount = beginning amount • e^( -lambda • time )
(where "e" is the mathematical constant 2.718281828...)
Ending Amount = 50 * 2.718281828^<span>(-0.0479470121*24 months)
</span><span>Ending Amount = 50 * 2.718281828^(-1.1507282904)
</span>Ending Amount = 50 * <span> <span> <span> 0.3164062499 </span> </span> </span>
Ending Amount = <span> <span> <span> 15.82</span></span></span> dollars
**********************************************************************
As a DOUBLE-CHECK we can work this out every 6 months:
0 months $50
6 months = $50 - (50 *.25) = 37.50
12 months = $37.50 -(37.50 *.25) = <span>28.125
18 months = $28.125 -(28.125 * .25) = 21.09375 </span>
24 months = $21.09375 -(21.09375 * .25) = <span> <span> <span> 15.8203125 </span> </span> </span>
You'll find this page quite helpful:
http://www.1728.org/halflif2.htm
We first must calculate half-life using the attached formula.
Half-Life = (time * ln(2)) / ln (beginning amount/ending amount)
Half-Life = (6 * 0.69314718056) / ln (50.00 / 37.50)
Half-Life = ( <span> <span> <span> 4.1588830834 </span> </span> </span> ) / ln ( <span> <span> <span> 1.3333333333 </span> </span> </span> )
Half-Life = ( <span> <span> 4.1588830834 </span> </span> ) / 0.28768207245
Half-Life = <span> <span> <span> 14.456525038 </span> </span> </span> months
Now we need to calculate "lambda"
lambda = ln(2) / half-life
lambda = 0.69314718056 / <span>14.456525038
lambda = </span><span><span><span>0.0479470121 </span> </span> </span>
Next we have to use this formula:
Ending Amount = beginning amount • e^( -lambda • time )
(where "e" is the mathematical constant 2.718281828...)
Ending Amount = 50 * 2.718281828^<span>(-0.0479470121*24 months)
</span><span>Ending Amount = 50 * 2.718281828^(-1.1507282904)
</span>Ending Amount = 50 * <span> <span> <span> 0.3164062499 </span> </span> </span>
Ending Amount = <span> <span> <span> 15.82</span></span></span> dollars
**********************************************************************
As a DOUBLE-CHECK we can work this out every 6 months:
0 months $50
6 months = $50 - (50 *.25) = 37.50
12 months = $37.50 -(37.50 *.25) = <span>28.125
18 months = $28.125 -(28.125 * .25) = 21.09375 </span>
24 months = $21.09375 -(21.09375 * .25) = <span> <span> <span> 15.8203125 </span> </span> </span>
You'll find this page quite helpful:
http://www.1728.org/halflif2.htm