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3 years ago

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 = ( 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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2b(k-1) Hope this helps!

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Health insurance benefits vary by the size of the company (the Henry J. Kaiser Family Foundation website, June 23, 2016). The sa

xxMikexx [17]

Answer:

$\chi^2 = \frac{(32-42)^2}{42}+\frac{(18-8)^2}{8}+\frac{(68-63)^2}{63}+\frac{(7-12)^2}{12}+\frac{(89-84)^2}{84}+\frac{(11-16)^2}{16}=19.221$

Now we can calculate the degrees of freedom for the statistic given by:

$df=(rows-1)(cols-1)=(3-1)(2-1)=2$

And we can calculate the p value given by:

$p_v = P(\chi^2_{2} >19.221)=0.000067$

And we can find the p value using the following excel code:

"=1-CHISQ.DIST(19.221,2,TRUE)"

Since the p values is higher than a significance level for example $\alpha=0.05$ , we can reject the null hypothesis at 5% of significance, and we can conclude that the two variables are dependent at 5% of significance.

Step-by-step explanation:

Previous concepts

A chi-square goodness of fit test "determines if a sample data matches a population".

A chi-square test for independence "compares two variables in a contingency table to see if they are related. In a more general sense, it tests to see whether distributions of categorical variables differ from each another".

Solution to the problem

Assume the following dataset:

Size Company/ Heal. Ins. Yes No Total

Small 32 18 50

Medium 68 7 75

Large 89 11 100

_____________________________________

Total 189 36 225

We need to conduct a chi square test in order to check the following hypothesis:

H0: independence between heath insurance coverage and size of the company

H1: NO independence between heath insurance coverage and size of the company

The statistic to check the hypothesis is given by:

$\sum_{i=1}^n \frac{(O_i -E_i)^2}{E_i}$

The table given represent the observed values, we just need to calculate the expected values with the following formula $E_i = \frac{total col * total row}{grand total}$

And the calculations are given by:

$E_{1} =\frac{50*189}{225}=42$

$E_{2} =\frac{50*36}{225}=8$

$E_{3} =\frac{75*189}{225}=63$

$E_{4} =\frac{75*36}{225}=12$

$E_{5} =\frac{100*189}{225}=84$

$E_{6} =\frac{100*36}{225}=16$

And the expected values are given by:

Size Company/ Heal. Ins. Yes No Total

Small 42 8 50

Medium 63 12 75

Large 84 16 100

_____________________________________

Total 189 36 225

And now we can calculate the statistic:

$\chi^2 = \frac{(32-42)^2}{42}+\frac{(18-8)^2}{8}+\frac{(68-63)^2}{63}+\frac{(7-12)^2}{12}+\frac{(89-84)^2}{84}+\frac{(11-16)^2}{16}=19.221$

Now we can calculate the degrees of freedom for the statistic given by:

$df=(rows-1)(cols-1)=(3-1)(2-1)=2$

And we can calculate the p value given by:

$p_v = P(\chi^2_{2} >19.221)=0.000067$

And we can find the p value using the following excel code:

"=1-CHISQ.DIST(19.221,2,TRUE)"

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Stock worth $80 a share dropped in value by 15% on Tuesday, then increased by $7 the next Wednesday and, finally, increased by 1

Nutka1998 [239]

<h2>Steps</h2>

So here are a couple expressions when a value changes by percentage (p = percentage in decimal form and m = original value):

When decrease: (1 - p)m
When increase: (1 + p)m

So firstly, the $80 share dropped by 15%. Since this is a decrease, follow the appropriate expression:

$15\%=0.15\\\\(1-0.15)*80\\0.85*80\\68$

On Tuesday, the share went from $80 to $68

Next, on Wednesday the share increased by $7. With this, just add $68 and 7.

$68+7=75$

On Wednesday, the share went from $68 to $75

Lastly, on Thursday the share increased by 12%. Since this is an increase, follow the appropriate expression:

$12\%=0.12\\\\(1+0.12)*75\\1.12*75\\84$

<h2>Answer</h2>

The final price of the share is $84.

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