Expert: Sherry Wallin - 2/3/2010

Question
QUESTION: I want to solve for n in the following problem

11800=10,000*(1.01^n) + 10n

I know how to solve this using a graphing calculator or computer and I have already done so.  However is there a way to explicitly solve this problem algebraically showing your work?  Thank you

ANSWER: Jason this problem is written incorrectly. Please resubmit written correctly.

Math Prof

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QUESTION: 11800 = 10000*(1.01)^n +10*n

I am not sure what you mean the problem is written incorrectly.  I want to know if there is anyway to solve for n explicitly besides approximation techniques.  I can enter y= 10000*(1.01)^x + 10*x - 11800 to find the solution in a graphing calculator.  

I guess basically what I am asking is is there a way to solve an equation y=A^x + B*x   provided that A and B are rational numbers.  Thank you for your help

ANSWER: 11800=10,000*(1.01^n) + 10n is what you sent originally, what you have sent now is:
11800 = 10000*(1.01)^n +10*n  which are NOT the same.
1.01^n and (1.01)^n are not the same. Note 1.01 = 1 + .01 so 1.01^n = 1 + .01^n.
What have you tried?

Math Prof

---------- FOLLOW-UP ----------

QUESTION: what i mean is the number (1.01)^n.

How would you solve this problem  11800=10000*(2)^n + 10*n

it really doesn't matter to me what the number is in the parentheses.  The question is can it be solved explicitly? besides using approximation methods like newtons or eulers method?  Thank you.

Answer
I don't think it can be solved explicitly because when you take the ln of both sides of the equation you get ln 11800 (which is just a number) = ln[(1.01)^n+10n] and there is no way algebraically to rewrite the ln[(1.01)^n+10n], sorry for all the confusion. It would have helped if you had asked if it could be done explicitly and I wouldn't have worried about what numbers you were using. Have a good day.

Math Prof