:) 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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the most boring thing ever written

step-by-step explanation:

i am writing something. yes, i plan to make it the most boring thing ever written. i go to the store. a car is parked. many cars are parked or moving. some are blue. some are tan. they have windows. in the store, there are items for sale. these include such things as soap, detergent, magazines, and lettuce. you can enhance your life with these products. soap can be used for bathing, be it in a bathtub or in a shower. apply the soap to your body and rinse. detergent is used to wash clothes. place your dirty clothes into a washing machine and add some detergent as directed on the box. select the appropriate settings on your washing machine and you should be ready to begin. magazines are stapled reading material made with glossy paper, and they cover a wide variety of topics, ranging from news and politics to business and stock market information. some magazines are concerned with more recreational topics, like sports card collecting or different kinds of hairstyles. lettuce is a vegetable.

$4034.40

the perimeter of the field is the sum of the lengths of the four sides:

47 yd + 158 yd + 47 yd + 158 yd = 410 yd

the cost of 3 ft (1 yd) of fence is 3×$3.28 = $9.84.

so the cost of jake's wood perimeter fance is

(410 yd) × ($9.84 /yd) = $4034.40