The function $P(x)=-4\mathrm{.}75x^2+3725x-5000$ gives the profit when $x$ units of a certain product are sold. Find

a$)$ the profit when $80$ units are sold

$$ dollars

b$)$ the average profit per unit when $80$ units are sold

$q,$ dollars per unit

c$)$ the rate that profit is changing when exactly $80$ units are sold

$$ dollars per unit

d$)$ the rate that profit changes on average when the number of units sold rises from $80$ to $160.$

$$ dollars per unit

e$)$ The number of units sold when profit stops increasing and starts decreasing. $($Round to the nearest whole number if necessary.$)$

units

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