document.write( "Question 93164: The US gross domestic product GDP in trillions of dollars is approximated by:
\n" ); document.write( "f(x)= -1.2155=3.7314 Lnx where x=5 corresponds to 1995. When will the GDP reach $12 Trillion?\r
\n" ); document.write( "\n" ); document.write( "Thanks in advance for your help\r
\n" ); document.write( "\n" ); document.write( "Sorry, this isn't from a text. \n" ); document.write( "
Algebra.Com's Answer #67813 by bucky(2189)\"\" \"About 
You can put this solution on YOUR website!
Given:
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\n" ); document.write( "\"f%28x%29+=+-1.2155%2B%283.7314%29%2ALn%28x%29\"
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\n" ); document.write( "[Hope that I interpreted it correctly and the = sign you have between the two terms
\n" ); document.write( "on the right side was meant to be a + sign]
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\n" ); document.write( "Set f(x) equal to 12
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\n" ); document.write( "\"12+=+-1.2155+%2B+%283.7314%29%2ALn%28x%29\"
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\n" ); document.write( "Get rid of the -1.2155 on the right side by adding 1.2155 to both sides:
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\n" ); document.write( "\"13.2155+=+3.7314%2ALn%28x%29\"
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\n" ); document.write( "Solve for Ln(x) by dividing both sides of this equation by 3.7314 to get:
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\n" ); document.write( "\"13.2155%2F3.7314+=+%283.7314%2F3.7314%29%2ALn%28x%29\"
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\n" ); document.write( "which after you do the divisions reduces to:
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\n" ); document.write( "\"3.5417+=+Ln%28x%29\"
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\n" ); document.write( "Just to have things in a little more conventional form, you can transpose the sides of
\n" ); document.write( "this equation to get the form:
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\n" ); document.write( "\"Ln%28x%29+=+3.5417\"
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\n" ); document.write( "Now you can solve for x by converting this logarithmic form to the equivalent exponential
\n" ); document.write( "form. To do this, you use the rule that says:
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\n" ); document.write( "\"Log%28b%2CN%29+=+y\" is equivalent to the exponential form \"b%5Ey+=+N\"
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\n" ); document.write( "In the natural logarithms b is defined as e (where e is 2.718281828 ...) and from your equation
\n" ); document.write( "you find that y = 3.5417 and N = x.
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\n" ); document.write( "Now take the exponential form and appropriately substitute the values for b, y, and N to
\n" ); document.write( "get that the exponential form of \"Ln%28x%29=3.5417\" is:
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\n" ); document.write( "\"e%5E%283.5417%29+=+x\"
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\n" ); document.write( "But \"e%5E%283.5417%29\" is just a constant that you can get from a scientific calculator.
\n" ); document.write( "If you enter 3.5417 and key the \"e%5Ex\" function on the calculator you find that the
\n" ); document.write( "answer is that x = 34.5256 is the number of years for the GNP to be $12 trillion.
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\n" ); document.write( "Now you need to interpret this. When x is 5, the year is 1995. So x = 34.5256 occurs
\n" ); document.write( "29.5245 years after x = 5. Therefore, add 29.5245 years to 1995 and you get 2024.5245.
\n" ); document.write( "This means that the economy should reach $12 trillion somewhere near the middle of the year
\n" ); document.write( "2024, and it will be slightly above the $12 trillion value at the start of 2025.
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\n" ); document.write( "Check the math here to see if I made any mistakes. The procedures used are correct.
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\n" ); document.write( "Hope this helps you to understand how you can solve the problem.
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