Let t be time in seconds and let r(t) be the rate, in gallons per second, that water enters a reservoir : r(t) = 600-30t
If the domain of r(t) is 0 <_t <_ 30, what is the range of r(t)?
since the function is linear, the range is the interval [r(0),r(30)]
or rather, since r is decreasing, [r(30),r(0)]
Question: does the water ever flow out? That is, can r(t) be negative? If not, then you have to truncate the range when r(t) = 0.
To find the range of r(t), we need to determine the possible values of r(t) for the given domain.
Given: r(t) = 600 - 30t, with the domain 0 ≤ t ≤ 30
Let's substitute the minimum and maximum values of t in the equation to find the range.
For t = 0:
r(0) = 600 - 30(0)
r(0) = 600
For t = 30:
r(30) = 600 - 30(30)
r(30) = 600 - 900
r(30) = -300
Therefore, the range of r(t) is -300 ≤ r(t) ≤ 600.
To find the range of r(t), we need to determine the possible values that r(t) can take. In this case, the function r(t) = 600 - 30t represents the rate at which water enters a reservoir, measured in gallons per second.
The domain of r(t) is given as 0 ≤ t ≤ 30, which means that the value of t can range from 0 to 30 (inclusive).
To find the range, we can substitute the minimum and maximum values of t into the function and calculate the corresponding values of r(t).
When t = 0:
r(0) = 600 - 30(0) = 600
When t = 30:
r(30) = 600 - 30(30) = 600 - 900 = -300
Therefore, the range of r(t) for 0 ≤ t ≤ 30 is from 600 to -300 gallons per second.