Question 469773
The answer to (a) hinges on the fact that {{{ log(-n) }}}
is impossible. There is no exponent with a positive base
that can give you a negative number.
Therefore, {{{ 1 - N/80 }}} cannot be negative.
This expression becomes negative when {{{ N > 80 }}},
so 80 words per minutes is the maximum possible.
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(b)
{{{ t = -62.5*ln(1 - N/80) }}}
Note here that {{{ ln( 1 - N/80 ) }}} MUST be negative in
order that {{{t}}} 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.
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Divide both sides by {{{ -62.5 }}}
{{{ ln(1 - N/80) = -t/62.5 }}}
I can rewrite this as:
{{{ e^(-t/62.5) = 1 - N/80 }}}
{{{ -N/80 = e^(-t/62.5) - 1 }}}
Multiply both sides by {{{ -80 }}}
{{{ N = 80*(1 - e^(-t/62.5)) }}}