The power output, PPP, of a prototype turbine is modeled by the function P(t)=15(t2+6),t≥0P(t) = \frac{1}{5}(t^2 + 6), \quad t \ge 0P(t)=51(t2+6),t≥0 where ttt is the time in hours since activation.
Find the range of PPP.
Find P−1(t)P^{-1}(t)P−1(t).
State the range of P−1(t)P^{-1}(t)P−1(t).
State the geometric transformation which maps the graph of y=P(t)y = P(t)y=P(t) onto the graph of y=P−1(t)y = P^{-1}(t)y=P−1(t).
Find the coordinates of the points of intersection of the graphs of y=P(t)y = P(t)y=P(t) and y=P−1(t)y = P^{-1}(t)y=P−1(t).