nitially at 50 ° F, which is placed in a 375 °F oven at 5:00 PM. After 75 min it is observed that the temperature of the roast {\ small T (t)} is 125 °F. When will the roast be at 150 ° F (medium done)?

Suppose an object moves along the y axis so that its location is y=f(x)=x²+x at time x (y is in meters, x is in seconds). Find (A) The average velocity (the average rate of change of y with respect to x) for x changing from 2 to 4. (B) The average velocity for x changing from 2 to 2+h. (C) The instantaneous velocity at x=2 second..

Suppose a spherical balloon is being filled with air so that its' volume and radius increase. t = time (in seconds) V = volume of the balloon at time t (in cm) T = radius of the balloon at time t (in cm) Restate the following sentence in terms of the above variables: "How fast the radius changing when the radius is 7 cm, if the balloon is being filled with air at a constant rate of 3 cm/s?" (Note: You do not need to solve the problem. Only determine what the question is asking, mathematically.) O What is if we know that r 7 and V = 3 ? O What is , given that r 7 and 3? O What is d when r 7, if d dt 3? O What is . if we know that r 7 and 33 O What is when r 7. given that 3?

The Population of a small town,p, is modelled by the function p(t)=10 050 + 255t-20t^2, where t is the time in years from now. Determine the average rate of change of the population from  a) year 0 to year 5 b) year 5 to year 8