The learning curves describes the rate at which a person learns certain tasks. If 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
a) according to this formula what is the maximum number of words per minute?
I have A correct at 80. How do I find b solve for N so N= what I can not get this part. Thank you for you help
t= - 62.5 In (1-N over 80)
To find the maximum number of words per minute (N) using this formula, we need to solve for N when t is at its highest value, which means taking the limit as t approaches infinity.
The formula you provided is: t = -62.5 ln(1 - N/80)
To solve for N, we can start by rearranging the formula:
t = -62.5 ln(1 - N/80)
t/(-62.5) = ln(1 - N/80)
ln(1 - N/80) = -t/62.5
Now, let's exponentiate both sides using the inverse of the natural logarithm. The exponentiation undoes the ln function, resulting in:
e^(ln(1 - N/80)) = e^(-t/62.5)
Simplifying further:
1 - N/80 = e^(-t/62.5)
Next, we isolate N by subtracting 1 and multiplying both sides by 80:
1 - 1 + N/80 = 80e^(-t/62.5)
N/80 = 80e^(-t/62.5) - 1
Finally, we multiply both sides by 80 to solve for N:
N = 80 * (80e^(-t/62.5) - 1)
Now, to find the maximum value of N, we need to evaluate this expression as t approaches infinity. As t becomes very large, the exponential term e^(-t/62.5) approaches zero, and the equation simplifies to:
N = 80 * (80 * 0 - 1)
N = -80
Therefore, the maximum number of words per minute (N) according to this formula is -80. However, note that a negative value for N doesn't make sense in the context of typing speed, so we can interpret this as there being no maximum value for N in this scenario.