Question 469773
a) max number of words is 80
domain of ln(x) is x>0
1-(N/80) > 0
1 > N/80
80 > N
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b) Use algebra to solve for N
{{{t=-62.5ln(1-(N/80))}}} 
Divide by -62.5 on both sides
{{{(-t)/62.5 = ln (1-(N/80))}}}
Rewrite in exponential form
{{{e^(-t/62.5) = 1 -(N/80)}}}
Add N/80 to both sides
{{{e^(-t/62.5) + (N/80) = 1}}}
Subtract e^(-t/62.5) to both sides
{{{N/80 = 1 - e^(-t/62.5)}}}
Multiply by 80 on both sides
{{{N = 80(1 - e^(-t/62.5))}}}