The signal strength SSS, measured in decibels (dB), of a satellite passing directly over a ground station is modeled by the function
S(t)=24−4∣5−t∣,t≥0 S(t) = 24 - 4|5 - t|, \quad t \ge 0 S(t)=24−4∣5−t∣,t≥0where t t\,t is the time in minutes since the signal was first detected.
Find the value of SS(8)SS(8)SS(8).
Solve the equation S(t)=2tS(t) = 2tS(t)=2t.
Given that the equation S(t)=kS(t) = kS(t)=k has exactly two distinct solutions for ttt, determine the range of possible values for the constant kkk.
A calibration adjustment transforms the signal graph into the graph with equation y=pS(t−q)y = pS(t - q)y=pS(t−q). The vertex of this transformed graph is at (1,12)(1, 12)(1,12). Find the value of the constants p p\,p and qqq.