Question 211361: I desperately need help. I have a 60 average right now and 2 weeks left. Please help me understand what I need to do. I have 2 weeks left to pass this class.
Evaluate the exponential equation for three positive values of x, three negative values of x, and at x=0. Show your work. Use the resulting ordered pairs to plot the graph; State the equation of the line asymptotic to the graph.
1. y= 5^x
2. y= log 7 ^x
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! Evaluate the exponential equation for three positive values of x, three negative values of x, and at x=0. Show your work. Use the resulting ordered pairs to plot the graph; State the equation of the line asymptotic to the graph.
1. y= 5^x
2. y= log 7 ^x
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PROBLEM NUMBER 1
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y = 5^x
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let x = -5, -3, -1, 0, 1, 3, 5
when x = -5, y = 5^(-5) = .00032
when x = -3, y = 5^(-3) = .008
when x = -1, y = 5^(-1) = .2
when x = 0, y = 5^0 = 1
when x = 1, y = 5^1 = 5
when x = 3, y = 5^3 = 5*5*5 = 125
when x = 5, y = 5^5 = 5*5*5*5*5 = 3125
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you find the x value of each pair and then the y value of each pair and you place your point on the intersection of the x value and y value.
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you do this for each coordinate pair in turn.
a coordinate pair would be an x value with its corresponding y value.
example:
when x = 3, y = 125
your coordinate pair is (3,125)
when x = -3, y = .008
your coordinate pair is (-3,.008)
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your graph will look like this:
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This graph has an asymptote at y = 0
as x gets more negative, y approaches 0 but never quite makes it.
when x = -10, y = 1.024 * 10^-7
when x = -100, y = 1.2676506 * 10^-70
y will approach 0 but never reaches 0 making y = 0 an asymptote of this equation.
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PROBLEM NUMBER 2
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y = log(7^x)
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This is the same as x * log(7) by one of the laws of logarithms that you would need to know.
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let x = -5, -3, -1, 0, 1, 3, 5 again.
when x = -5, y = -5*log(7) = -4.2254902
when x = -3, y = -3*log(7) = -2.53529412
when x = -1, y = -1*log(7) = -.84509804
when x = 0, y = 0*log(7) = 0
when x = 1, y = 1*log(7) = .84509804
when x = 3, y = 3*log(7) = 2.53529412
when x = 5, y = 5*log(7) = 4.2254902
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you find the x value of each pair and then the y value of each pair and you place your point on the intersection of the x value and y value.
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you do this for each coordinate pair in turn.
a coordinate pair would be an x value with its corresponding y value.
example:
when x = 3, y = 2.53529412
your coordinate pair is (3,2.53529412)
when x = -3, y = -2.53529412
your coordinate pair is (-3,-2.53529412)
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your graph will look like this:
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This graph looks like a straight line.
logarithms do that.
They take an exponential equation and make them look like straight lines when you take the log of them.
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A graph of 7^x would look like this:
The graph of log(7^x) looks like this:
when x = 5, y = 7^x = 16807 while y = log(7^x) = 4.2254902
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This has to do with the nature of logarithms.
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The basic formula for logarithms is that the log(x) = y if and only if 10^y = x
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An example:
log(1000) = 3 if and only if 10^3 = 1000
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In our formula, we have:
log(7^5) = log(16807) = 4.2254902
This means that 10^4.2254902 = 16807.
You can use your calculator to prove this is true.
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The equation of log(7^x) does not have an asymptote.
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A fairly decent definition of asymptote can be found at the following web address:
http://www.wordiq.com/definition/Asymptote
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If you need extra help with understanding exponents and logarithms, or any other topics in algegbra, then you can go to the following website where help would be available.
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http://www.wtamu.edu/academic/anns/mps/math/mathlab/col_algebra/index.htm
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The tutorials you would be interested in dealing with exponents would be:
Tutorial 2,5,19,42,45,47
The tutorials you would be interested in dealing with logarithms would be:
43,44,46,47
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If this website doesn't suit your fancy, you can find others by doing a search on "algebra tutorials" or "algebra lessons" or on anything you are having trouble with, like "exponential equations" or "logarithms" or "logarithmic equations".
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