The output signal RRR, measured in millivolts, of a high-precision sensor is modeled by the function
R(t)=12tln(4t)t>0 R(t) = 12\sqrt{t} \ln(4t) \quad t > 0 R(t)=12tln(4t)t>0where ttt is the time in milliseconds after the sensor is triggered. The signal is zero at time TTT.
State the value of TTT.
The signal reaches its minimum value at the point MMM.
Use calculus to find the exact coordinates of MMM.
Hence find the range of the function S(t)S(t)S(t) where
S(t)=−5R(t) S(t) = -5R(t) S(t)=−5R(t)
