The given function represents the percent of the software download left to complete. Here, t is the time in minutes, and p is the percent of the process left to complete.
We are asked to find where the function meets the horizontal axis, which is the t-value that makes p=0. We can find it by substituting 0 for p.
In order to graph this function, we need to find its intercepts. The vertical axis is represented by p, and the horizontal axis by t. We already found the intersection with the horizontal axis in Part A. Let's now substitute 0 for t to find the intersection with the vertical axis.
The intersection with the vertical axis occurs at the point (0,100). Now, we will plot the intercepts and connect them with a line to obtain the graph of the function. Note that, in the context of the problem, neither t nor p can be negative.
We found in Part A that the x-intercept is at 16 minutes. This means that, after 16 minutes, the percent of the process left to complete will be zero. In other words, the process takes 16 minutes to complete.
We can use the graph in Part B, to find the domain and range of the function.
We see that t can take any value from 0 to 16, inclusive. We also see in the graph that p can take any value between 0 and 100, inclusive.
D: R: 0≤t≤160≤p≤100