Question on a Oil Leak
A tractor has an oil leak. The amount of oil, L(t), in milliliters per hour that leaks out is a function of the tractor's operating temperature, t, in degrees Celsius. The function is
L(t)= 0.0004t^2+0.16t+20,100 degrees Celsius<_t<_160 degrees Celsius
a) How many milliters of oil will leak out in 1 hour if the operating temperature of the tractor is 100 degrees C?
b) If oil is leaking out at 53 milliliters per hour, what is the operating temperature of the tractor?
a) t = 100 ºC
L = 0.0004(100)^2+0.16*100+20
L = 4 + 16 + 20 = 40
L = 40 ml/hr
b) L = 53 ml/hr
53 = 0.0004t^2+0.16t+20 <--- let t = 100T
53 = 4T^2 + 16T + 20
4T^2 + 16T - 33 = 0
(2T - 3)(2T + 11) = 0
T = 1.5, T = -5.5
t = 150, t = -550 (ignore the negative temperature)
t = 150 º