A rocket ship is speeding away from the sun. In convenient units, the radiation R inside the ship is given by
R = 1/x^2, where x is the distance to the sun. This distance x, as a function of time t in hours, is given by x = 12t+ 2.
How far is the ship from the sun when the radiation level is decreasing at a rate of 3 units per hour, when dR/dt =-3?
What does x=___?
Use the chain rule here:
Now, with dR/dx=-2/x^3 and dx/dt=12, then we have the following:
When dR/dt=-3, we see ...
Given the distance to the sun of a rocket as a function of time, and the radiation inside the ship as a function of the distance to the sun, we find the distance to the sun when the radiation level is decreasing at a rate of 3 units per hour