What Value of t Makes N(t) Equal to 250?

[needingtoknow]

Homework Statement

What value of t will make the function = 250?

N(t) = 500 / (1+9e^(-5t))
250 = 500 / (1+9e^(-5t))

The Attempt at a Solution

1 + 9e^-5t = 2
9e^-5t = 1
t = log1/log(-5)(9e)
t = 0

However t = 0 is incorrect because when it is subbed back into the original equation it does not result in 250. How do I solve for the correct value of t?

 

[Millennial]

Your solution is difficult to follow. Everything up to your second step checks out, but I can't understand how you went from the second equation to the third. The third equation also seems completely senseless. You can't take the natural logarithm of a negative number in the real number line.

If you show your full transition from the second step to the third, we might be able to help you better. But a wild guess from my head suggests that you are somehow misreading the second equation, so I will write it down nicely: $9e^{-5t} = 1$. Did that help?

 

[SteamKing]

Your are correct to this point:

9e^(-5t) = 1

You didn't apply logarithms correctly after this. Here is how to proceed correctly:

e^(-5t) = 1/9
Mod note: Deleted the remainder of this post, as it was probably too much help.
Now take the natural log of both sides: