Let P (t) represent the amount of a certain drug, in milligrams, that is in the bloodstream at time t hours. The rate at which the drug leaves the bloodstream is proportional to the amount of the drug in the bloodstream. The amount of the drug in the bloodstream can be modeled by dP/dt = kP, where k is a constant and t is time, in hours. At time t = 0,500 milligrams of the drug was administered. At the moment when the amount of the drug in the bloodstream is 50 milligrams, the amount is decreasing at a rate of 11.5 milligrams per hour. Required:
What is an expression for P (t)?

Solve the system of equations. y= 2x y= x^2 - 15

Michelle and julie work at a catering company. they need to bake 264 cookies for a birthday party that starts in a little over an hour and a half. each tube of cookie dough claims to make 36 cookies, but michelle eats about 1/5 of every tube and julie makes cookies that are 1.5 times as large as the recommended cookie size. it takes about 8 minutes to bake a container of cookies, but since julie's cookies are larger, they take 12 minutes to bake. a. how many tubes should each girl plan to bake? how long does each girl use the oven? b. explain your solution process what did you make? c. what assumptions did you make?

The? half-life of a radioactive substance is 20 years. if you start with some amount of this? substance, what fraction will remain in 120 ? years