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About Scott A Wilson
Expertise
I can answer any question in algebra, pre-calculus, probability, trigonometry, or statistics.

Experience
Experience in the area; I have tutored people over the years in algebra, basic math, and statistics. I worked at The Boeing Company for over 5 years. Education/Credentials: MS degreee in Mathematics from Oregon State Univeristy; taken well over 100 hours of upper division credits in mathematical courses such as calculus, statistics, probabilty, linear algrebra, powers, linear regression, matrices, and more. I graduated with honors. Past/Present Clients: College Students at OSU, various math people since college, over 700 people in math and calculus.

You are here: Experts > Science > Mathematics > Advanced Math > Algebra

Topic: Advanced Math

Expert: Scott A Wilson
Date: 5/13/2008
Subject: Algebra

Question
To follow up on the instruction you provided me with on 5/10. How would I physically graph this? On e^x, note that as x gets extremely negative, e^x gets close to zero from the positive side (above the x axis). At 0, the function is 1. On the positive side, it quickly goes up faster and faster all of the time as x gets greater. The ln (x) function is the inverse of e^x, so draw a line x=y. The function treats this line like a mirror.

When x is doubled, the curve is increased in the x direction by around eight times.

Answer
On the left side of the graph paper, start on the x-axis. Move across, slowly increasing to one when you get to zero. After you got through one, keep drawing to the light increasing the line faster and faster as you go. This is e^x.

Draw the line x=y. The graph of ln(x) looks just the same, but on the other side. Also, the following table may help. These tables have the deciamls lined up at this end, but lost a little bit when I send them.

x e^x
-3 0.05
-2 0.14
-1 0.37
0 1.00
1 2.72
2 7.39
3 20.09

   x   ln(x)
0.125 -2.08
0.250 -1.39
0.500 -0.69
  1    0.00
  2    0.69
  3    1.10

Note that 0.125=1/8, 0.25=1/4, and 0.5=1/2. The e^x values and ln(x) values are for constructing two different graphs. All that needs to be done is plotting the values and connecting them with a smooth curve.

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