Plug the given t-values into the given formula
1. Let t be in seconds and let r(t) be the rate< in gallons/second, at which water enters a reservoir. We are given that, for t 0<t<30,: r(t) = 800 - 40t
1. evaluate the expressions r(0), r(15), r(25) and explain their physical significance.
, and simplify to find the r-values.
Keeping in mind that "t" is defined as the time in seconds and "r" is defined as the rate of flow in gallons per second, state the r- and t-value pairs in terms of rate of flow r at a given time t. For instance, the value of r(5) would be the rate of flow, in gallons per second, at a time of five seconds.
2. if you were to graph y=r(t) for 0<t<30, labeling the intercepts. What is the physical significance of the slope and the intercepts?
To learn about the meaning of slope and y-intercept in the context of word problems, try here
(well, okay; the t-intercept) is of course when r (usually y) equals zero. What does "r" stand for? What does "t" stand for? Interpret this intercept in terms of the rate of flow at that time t.
3. for 0<t<30, when does the reservoir have the most water? When does it have the least water?
Look at the graph
. When (at what t-value) is the line the highest? When is it the lowest?
4. What are the domain and range of r?
They gave you the domain when they gave you the restrictions on t. To find the range
, find the output values over the interval
for which the function is defined.
Yes, "y = 800 - 40x" is defined "everywhere", but that isn't the domain they gave you. And yes, "y = 800 - 40x" goes "everywhere" (eventually attains every possible y-value), but that won't happen over the domain they gave you. So use the highest and lowest values from part (3) to state the range for r(t).
If you get stuck, please reply showing your work and reasoning so far. Thank you!