A cell phone manufacturer predicts pre-orders of their new cell phone using the function: P(d)=-2\sqrt(-d)+20
P=pre-orders(in millions) of the phone
d=days before the release date
*if you search the graph up on desmos or a graphing site you will see the y coord. goes up to 20.
a) Indicate what the domain and range are meant for in this context. What do they show/explain?
b)Determine the number of pre-orders that the company can expect, 40 days before the release date of the cell phone.
It appears you have intended that
p(d) = -2/√(-d) + 20
(a) since √x is undefined for x<0, I assume d is really the number of days after release, so that -d is positive before the release. The range means that pre-orders go down as the release date gets near.
(b) p(-40) = 20-2/√40 = 19.68
Thank you for making sense out of that oobleck.
Apologies I couldn't figure out how to create the square root sign on my pc. Thank you for the understanding of the range.
a) In this context, the domain refers to the set of possible values for the number of days before the release date (d), while the range refers to the set of possible values for the number of pre-orders (P). The domain helps to establish the possible inputs for the function, indicating the range within which the number of days before the release date can vary. The range, on the other hand, represents the possible outputs or values for the number of pre-orders, providing information about the predicted popularity of the phone at different time points.
b) To determine the number of pre-orders that the company can expect 40 days before the release date of the cell phone, we need to substitute the value of d into the given function P(d).
Plug d = 40 into the function P(d):
P(40) = -2√(-40) + 20
Before we can continue, we need to address an issue with the given function. The function P(d) involves a square root, and it is not defined for negative numbers. Since we cannot have a negative number of days before the release date, we need to consider the function's validity within the given context.
Since the function has a square root of -d, it implies that the domain of the function should be restricted to positive values of d.
So, if we use the revised domain of d ≥ 0, we can compute the value of P(40) as follows:
P(40) = -2√(-40) + 20
As √(-40) is undefined within the domain we've established, we disregard the terms involving the square root.
P(40) = 20
Therefore, the number of pre-orders that the company can expect 40 days before the release date is 20 million.