# First Order Differential Equation

EV33
Ok so we are given a word problem discussing compound interest. In the first part of the question, we are given the equation:
S(t) = (k/r)(e^rt -1)
The next thing we are asked to do is calculate the value of r are given values of k, t, and
S(t). The given values are k = 2000, t = 40, S(t) = 10^6.
Plugging the values into this equation, you get:
10^6 = (2000/r)(e^40r - 1)

So far I have divided both sides by 2000 so that the equation is now:
500 = (1/r)(e^40r -1)

However now I can not figure out how to solve the equation for r with the two locations of the r's in the problem. Please help.

Thanks.

Homework Helper
You can't solve that using algebra and simple functions. You'll have to solve it numerically. Or graph the function and figure out where it crosses 500. I'd concentrate near small numbers like r=0.01.

EV33
What do you mean by solving it numerically?