A tank contained 80 liters of water. The function w represents the relationship between t, time in minutes, and the amount of water in the tank in liters. The equation w(t)=80-2.5t defines this function.[br]1. How much water will be in the tank after 13 minutes?[br]2. How many minutes will it take until the tank has 5 liters of water?[br]3. In this situation, what information can we gain from the inverse of function w?[br]4. Find the inverse of function w. Be prepared to explain or show your reasoning.[br]5. How would the graph of the inverse function of w compare to the graph of w? Describe or sketch your prediction.
1. 47.5 liters[br]2. 30 minutes[br]3. Sample response: The inverse of function w can help us find the time it takes for the water in the tank to reach a certain amount of water.[br]4. t=(80-w(t))/2.5[br]5. Sample response: The quantities represented by the horizontal and vertical axes would be reversed. The graph would still be a line that slants downward, but the vertical and horizontal intercepts would be different. The values of each coordinate pair would be the reverse of those in the graph of w.