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nadezda [96]
3 years ago
7

Please help :) this is exponential decay 10 pts

Mathematics
2 answers:
Elan Coil [88]3 years ago
7 0

$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 = ( 4.1588830834 ) / ln ( 1.3333333333 )

Half-Life = ( 4.1588830834 ) / 0.28768207245

Half-Life = 14.456525038 months


Now we need to calculate "lambda"

lambda = ln(2) / half-life

lambda = 0.69314718056 / 14.456525038

lambda = 0.0479470121


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^(-0.0479470121*24 months)

Ending Amount = 50 * 2.718281828^(-1.1507282904)

Ending Amount = 50 * 0.3164062499

Ending Amount = 15.82 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) = 28.125

18 months = $28.125 -(28.125 * .25) = 21.09375

24 months = $21.09375 -(21.09375 * .25) = 15.8203125


You'll find this page quite helpful:

http://www.1728.org/halflif2.htm



Read more on Brainly.com - brainly.com/question/9917873#readmore

VMariaS [17]3 years ago
5 0
$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


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