Answer
The unit is gallons per hour
Work Step by Step
The function of time is given by:
$v(t) = 100,000(1 - \frac{1}{60}t)^{2}$
To find the rate, we have to differentiate the above equation :
$v^{'}(t) ~= 200,000(1 - \frac{1}{60}t)(-\frac{1}{60})$
$~~~~~~~~~= - \frac{20,000}{6}(1-\frac{1}{60}t)$
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Substitute each value to the equation:
$v^{'}(0) ~=- \frac{20,000}{6}(1-\frac{1}{60}t)$
$~~~~~~~~~=- \frac{10,000}{3}$
$v^{'}(10) ~=- \frac{20,000}{6}(1-\frac{1}{60}t)$
$~~~~~~~~~~~=- \frac{25,000}{9}$
$v^{'}(20) ~=- \frac{20,000}{6}(1-\frac{1}{60}t)$
$~~~~~~~~~~~=- \frac{20,000}{9}$
$v^{'}(30) ~=- \frac{20,000}{6}(1-\frac{1}{60}t)$
$~~~~~~~~~~~=- \frac{5000}{3}$
$v^{'}(40) ~=- \frac{20,000}{6}(1-\frac{1}{60}t)$
$~~~~~~~~~~~=- \frac{10,000}{9}$
$v^{'}(50) ~=- \frac{20,000}{6}(1-\frac{1}{60}t)$
$~~~~~~~~~~~=- \frac{5000}{9}$
$v^{'}(60) ~=- \frac{20,000}{6}(1-\frac{1}{60}t)$
$~~~~~~~~~~~=0$
The greatest rate is at $t=0$, the least is $t = 60$
