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Report on 2009 World Market Forecasts for Imported Compounded Rubber with Unvulconized Carbon Black or Silica in Primary Forms or in Plates Sheets or Strip ( http://www.bharatbook.com/Market-Research-Reports/Report-on-2009-World-Market-Forecasts-for-Imported-Compounded-Rubber-with-Unvulconized-Carbon-Black-or-Silica-in-Primary-Forms-or-in-Plates-Sheets-or-Strip.html ) provides information about the market of compounded Rubber.
 
 
 This report was created for strategic planners, international marketing executives and export managers whose primary concern is the world market for compounded rubber with unvulconized carbon black or silica in primary forms or in plates, sheets, or strip. With the globalization of this market, managers can no longer be contented with a local view. Nor can managers be contented with out-of-date statistics that appear several years after the fact. A methodology is developed, based on macroeconomic and trade models, to estimate the market for compounded rubber with unvulconized carbon black or silica in primary forms or in plates, sheets, or strip for those firms serving the world via exports and foreign direct investment. It does so for the current year based on a variety of key historical indicators and econometric models.
 
 In what follows, this report begins by summarizing the world exporter’s market for compounded rubber with unvulconized carbon black or silica in primary forms or in plates, sheets, or strip. The total level of exports on a worldwide basis is based on a model that aggregates across over 150 key country markets and projects these to the current year. From there, each country represents a percent of the world market. This market is served from a number of competitive countries of origin. Based on supply-side dynamics, market shares by country of origin are then calculated across each country market. These shares lead to a volume of import values for each country and are aggregated to regional and world totals. In doing so, we are able to obtain maximum likelihood estimates of both the value of each market and the shares that competitors (countries serving that market) are likely to receive this year. From these figures, world rankings are calculated to allow managers to prioritize markets. In this way, all the figures provided in this report are forecasts that can be combined with internal information for strategic planning purposes. Of the 150 countries considered, if a country is not reported here it is therefore estimated to have only a negligible level of trade in compounded rubber with unvulconized carbon black or silica in primary forms or in plates, sheets, or strip (i.e. their market shares are close or equal to zero percent). “Compounded Rubber with Unvulconized Carbon Black or Silica in Primary Forms or in Plates, Sheets, or Strip” as a category is defined in this report following the definition given by the United Nations Statistics Division Classification Registry using the Standard International Trade Classification, Revision 3 (SITC, Rev. 3). The SITC code that defined “compounded rubber with unvulconized carbon black or silica in primary forms or in plates, sheets, or strip” is 62111 . This report is updated on an annual basis.
 
 For more information please visit : http://www.bharatbook.com/Market-Research/Rubber.html
 
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Article Source: ArticlesBase.com - Compounded Rubber With Unvulconized Carbon Black or Silica in Primary Forms - Forecast & Analysis

Creating Exponential Functions Part 2

carbon 14 dating calculator

need some help to make sure for some of my answers and explaination to others ..?

(>) is for my answers
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1. ln(e^1.618) =
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>1.618 is there any explaination to how to find it without using the calculator??
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2. Sharon invest $2500 at an annual interest rate 9%. how much is tl investment worth after 10 years if the inter is compounded continuously?
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>i use this formula A=Pe^rt, =614.9
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3. The age of an artifact can be determined using carbon-14 dating with the equation N(t)=N(0)e^-0.00012t. What is the approximate age of an artifact if a sample reveals that it contains 34% of its original carbon-14?
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>i didnt understand this question?!?!
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4.log(x)1/128=-7
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>x=2
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5.xlog1/6=log6
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>x=-1
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6.ln(2x)=4ln2
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>x=8
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7.lnx^0.5 - 3=1
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>?????
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8. ln(x+1)=2ln4
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>x=15
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9. logx+log(x+3)=1
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>????
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10.3^x=5^2.3
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>x=3.3695
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thank you very much for your time, i really appreciate it

1) ln.x and e^x are the opposites of each other - so ln.(e^x) = x.
Just like if I said what is x * (8 / x) you know the answer is 8 because dividing by x is the opposite of multiplying by x.

2) Your answer must be wrong, as you’ve ended up with less money than she started with ($2500)! And you’d expect that after investing for 10 years at a good rate of interest (9%) you’d have more money. So that should make you think and check your method.
The formula you’ve written is wrong - you don’t need e in the equation.
I would use this equation:
A = P * r^t
P is the original investment, 2500.
r is 9% which as a multiplication factor is 1.09 (because after each year, you add 9%, so you have 109% total compared to the start, and 109% = multiply by 1.09).
t is 10 (years).
So A = 2500 * (1.09 ^ 10) = 2500 * 2.367 = $5918

3) Well, you have the formula, you just need to work out how the information in the question relates to it. N(t) is the amount of C14 left after t years. N(0) is the amount you had t the start. You’re told that N(t) is 34% of N(0), so if we divide both sides of the equation by N(0) we get:
N(t) / N(0) = 34% = 0.34 = e^-0.00012t
Take the natural log of each side:
ln0.34 = -1.0788 = ln(e^-0.00012t) = -0.00012t
So t = -1.0788 / -0.00012 = 8990 years.

4), 5) and 6) are all correct.

7) Add 3 to both sides, and remember that lnx^y = ylnx
So:
0.5 ln x = 1+3 = 4
lnx = 8
x = e^8 = 290.96

and 10) are correct.

9) remember ln(A + B) = lnA*lnB
So logx + log(x+3) = logx + logxlog3 = logx(1 + log3) = 1
I presume you’re using the convention that log means log (base 10) - if not you’ll have to correct the answers from here on
log x = 1/(1 + log3) = 1/(1 + 0.4771) = 0.6770
So x = 10^0.6770 = 4.75

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