SOLUTION: The "learning curve" describes the rate at which a person learns certain tasks. If a person sets a goal of typing N words per minute (wpm), the length of time t (in days) to achiev

Question 469773: The "learning curve" describes the rate at which a person learns certain tasks. If a person sets a goal of typing N words per minute (wpm), the length of time t (in days) to achieve this goal is given by the following formula.
t=-62.5ln(1-N/80)
(a) According to this formula, what is the maximum number of words per minute?

(b) Solve for N.
I am trying to remedy this question to no end.Can someone please help me? thanks!
Found 2 solutions by ccs2011, josmiceli:
Answer by ccs2011(207) (Show Source): You can put this solution on YOUR website!
a) max number of words is 80
domain of ln(x) is x>0
1-(N/80) > 0
1 > N/80
80 > N
*******************************
b) Use algebra to solve for N

Divide by -62.5 on both sides

Rewrite in exponential form

Add N/80 to both sides

Subtract e^(-t/62.5) to both sides

Multiply by 80 on both sides

Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
The answer to (a) hinges on the fact that
is impossible. There is no exponent with a positive base
that can give you a negative number.
Therefore, cannot be negative.
This expression becomes negative when ,
so 80 words per minutes is the maximum possible.
-----------------
(b)

Note here that MUST be negative in
order that come out positive, since (-)x(-) = (+)
A log can certainly be negative, and it will give you a
result that is less than 1, but never a negative result
as I just stated.
-------------
Divide both sides by

I can rewrite this as:

Multiply both sides by

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