Answer:
Domain of the first statement = [0, ∞]
Domain of the second statement = [0, 13]
Domain of the third statement = [0, 30]
Explanation:
The complete question is given as
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used. Identify the domain for each of the given functions. [0, 150], [0, 65], [0, 30], [0,∞], [0, 13]
- The function S(t) describes the number of subscribers of a video streaming service, where t is the number of weeks since the launch of the website.
S(t) = 65 (1.25)ᵗ
A local animal shelter initially housed 65 puppies that were made available for adoption. The function P(t) describes the current number of puppies available for adoption, where t is the number of days since the puppies were made available.
P(t) = 65 - 5t
- An event center charges a flat $65 fee plus $5 per guest to rent a conference room with a maximum capacity of 30 guests. The function C(t) describes the cost of renting the room, where t is the number of guests.
C(t) = 65 + 5t
The domain of a function refers to the region of values of the independent variable where the function can take on realistic values.
It refers to the interval of numbers where the independent variable will enter the function and give realistic solutions for the function.
For the first statement, the function S(t) gives the number of subscribers for a steaming service as a function of the number of weeks since launch.
S(t) = 65 (1.25)ᵗ
The number of weeks since launch is a time value, which cannot be negative. Looking at the function, this expression will always give a realistic answer as long as t ranges from 0 to infinity. So, the domain of this expression where there are answers for different values of t would be [0, ∞]
For the second statement, the function P(t) represents the number of puppies available for adoption as a function of the time (number of days) since the puppies were made available for adoption.
P(t) = 65 - 5t
This function shows that the time since the puppies were too, cannot be negative, so, it will also start from the number 0 which will give a value of P = 65; indicating that there are 65 puppies up for adoption at the start of it all. The function shows that as t increases, the number of puppies still available for adoption reduces. The function will reach its limit when there are no longer puppies available for adoption.
That is, when P = 0
At P=0,
P(t) = 65 - 5t = 0; t = 13.
This shows that the 65 puppies are all adopted by the 13th day since they were put up for adoption. And since P(t) cannot take on negative values (number of puppies available for adoption cannot be negative), the domain for this function will be [0, 13]. From day 0 since the puppies were made available for adoption where there are 65 puppies to day 13 when all the puppies are adopted.
For the third statement, the cost function, C(t) represents the cost of renting a room which is a function of the number of guests, t. It has two parts; a flat rate of $65 irrespective of the number of guests and a rate of $5 per guest.
C(t) = 65 + 5t
It is also given in the question that the maximum number of guests allowable in the room is 30.
This means that the number of guests (which is the independent variable) can vary from a value of 0 to a value of 30.
From the definition of domain provided at the beginning, it is evident that the domain of this function is [0, 30]. The values that the independent variable can take on to give a realistic answer for the function.
Hope this Helps!!!