The R$.$C$.$ Helliot Advertising Company finds that its profits on day $t$ of an advertising campaign is given by $P(t)=-4t^2+80t+48,000$ where $P(t)$ is profit in dollars for day $t$ of the campaign.

A$)$ Find a simplified expression for the marginal profit function. $($Be sure to use the proper variable in your answer.$)$

$MP(t)=$

B$)$ What is the exact rate of change of profits when $25$ days have been passed in the campaign? The rate of change is dollars per day. $($Your answer may be negative.$)$

$($C$)$ What are their total profits on day $25$ of the campaign?

Total profits on day $25$ are