The temperature, $T,$ in degrees Fahrenheit, in a car's radiator during the first $4$ minutes of driving is a function of time, $t.$ The temperature can be found by the formula $T=6\mathrm{.}1t^2+14t+32,0t4$

a$)$ What is the car radiator's temperature at the instant the car is turned on$?$

b$)$ What is the car radiator's temperature after the car has been driven for $3$ minutes?

c$)$ How long after the car has begun operating will the car radiator's temperature reach $150F?$