:) this is exponential decay 10 pts

$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

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