You can
put this solution on YOUR website!Given:
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[Hope that I interpreted it correctly and the = sign you have between the two terms
on the right side was meant to be a + sign]
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Set f(x) equal to 12
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Get rid of the -1.2155 on the right side by adding 1.2155 to both sides:
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Solve for Ln(x) by dividing both sides of this equation by 3.7314 to get:
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which after you do the divisions reduces to:
.
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Just to have things in a little more conventional form, you can transpose the sides of
this equation to get the form:
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Now you can solve for x by converting this logarithmic form to the equivalent exponential
form. To do this, you use the rule that says:
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is equivalent to the exponential form
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In the natural logarithms b is defined as e (where e is 2.718281828 ...) and from your equation
you find that y = 3.5417 and N = x.
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Now take the exponential form and appropriately substitute the values for b, y, and N to
get that the exponential form of
is:
.
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But
is just a constant that you can get from a scientific calculator.
If you enter 3.5417 and key the
function on the calculator you find that the
answer is that x = 34.5256 is the number of years for the GNP to be $12 trillion.
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Now you need to interpret this. When x is 5, the year is 1995. So x = 34.5256 occurs
29.5245 years after x = 5. Therefore, add 29.5245 years to 1995 and you get 2024.5245.
This means that the economy should reach $12 trillion somewhere near the middle of the year
2024, and it will be slightly above the $12 trillion value at the start of 2025.
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Check the math here to see if I made any mistakes. The procedures used are correct.
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Hope this helps you to understand how you can solve the problem.
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