SOLUTION: Find the solution of the exponential equation 100 (1.02)^(2t) = 50,000

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Find the solution of the exponential equation 100 (1.02)^(2t) = 50,000      Log On


   

Question 877637: Find the solution of the exponential equation
100 (1.02)^(2t) = 50,000
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39808) About Me  (Show Source):
You can put this solution on YOUR website!
What you should already know:

100%281.02%29%5E%282t%29=50000
%28100%2F100%291.02%5E%282t%29=50000%2F100
1.02%5E%282t%29=500


What you are studying how to do now:
log%28%281.02%5E%282t%29%29%29=log%28%28500%29%29
2t%2Alog%28%281.02%29%29=log%28%285%2A10%5E2%29%29
2t%2Alog%28%281.02%29%29=2%2Alog%28%285%2A10%29%29
t%2Alog%28%281.02%29%29=log%28%285%2A10%29%29
t=log%28%285%2A10%29%29%2Flog%28%281.02%29%29
How to continue this depends on what base you want. Base ten might be most convenient.

t=%28log%2810%2C5%2A10%29%29%2F%28log%2810%2C1.02%29%29

t=%28log%2810%2C5%29%2Blog%2810%2C10%29%29%2F%28log%2810%2C1.02%29%29

highlight%28t=%28%28log%2810%2C5%29%29%2B1%29%2Flog%2810%2C1.02%29%29

Answer by MathTherapy(10818) About Me  (Show Source):
You can put this solution on YOUR website!

Find the solution of the exponential equation
100 (1.02)^(2t) = 50,000


highlight_green%28t+=+%28log+500%29%2F%282%2Alog+1.02%29%29, or highlight_green%28t+=+156.9137268%29

You can do the check!! 



If you need a complete and detailed solution, let me know!!



Send comments, “thank-yous,” and inquiries to “D” at MathMadEzy@aol.com.

Further help is available, online or in-person, for a fee, obviously.