The sales(in millions) of a DVD recording of a hit movie t years from the date of release is given by
a) Find the rate of which the sales are changing at time t.
b) How fast are the sales changing at the time the DVDs are released?
c) How fast are the sales changing two years from the date of release?
a) Well, the rate at which the sales are changing at time t would depend on the derivative of the sales function with respect to time. So, we need the sales function to calculate that. Do you have the sales function or any information about it?
b) Ah, the age-old question: How fast are the sales changing at the time the DVDs are released? It's like asking how fast a baby will grow when it's just been born. Let's just say the sales are gonna start slow, and it's gonna take some time for them to pick up speed. So, maybe give it a few weeks or months before asking this question again.
c) Two years from the date of release, huh? Well, if a movie is still selling DVDs after two years, it must be doing pretty well, right? I mean, it's not like those movies that end up in the bargain bin within a month. So, the sales are probably still going strong, but maybe not as fast as they were initially. I guess it depends on the movie and its popularity.
To answer these questions, we need to differentiate the given function with respect to time (t).
Let's assume the sales function is S(t) (in millions), where t is the time in years since the release of the DVD.
a) To find the rate at which the sales are changing at time t, we differentiate S(t) with respect to t: dS(t)/dt.
b) To find how fast the sales are changing at the time the DVDs are released (t = 0), we evaluate dS(t)/dt at t = 0.
c) To find how fast the sales are changing two years from the date of release (t = 2), we evaluate dS(t)/dt at t = 2.
However, since you have not provided the sales function, we cannot derive the derivative and provide a direct answer to these questions. Please provide the sales function, and we can proceed with the calculations.
To find the rate at which the sales are changing at a particular time t, we need to differentiate the sales function with respect to time t.
Let's assume the sales function is called S(t), where t represents the time in years since the release of the movie.
a) To find the rate at which the sales are changing at time t, we need to find the derivative of S(t) with respect to t, denoted as dS/dt. This will give us the instantaneous rate of change of sales at any given time.
b) To find how fast the sales are changing at the time the DVDs are released, we need to find the value of dS/dt at t = 0. This represents the rate of change of sales at the moment of release.
c) To find how fast the sales are changing two years from the date of release, we need to evaluate dS/dt at t = 2. This will give us the rate of change of sales at that particular time.
It's important to note that in order to find the derivative dS/dt, we need to know the specific mathematical equation or expression for the sales function S(t). Once we have that, we can differentiate it to find the rate of change at any specific time.