Question

The rate of change of P with respect to t is directly proportional to (10 - t) and inversely proportional to the cube root of P. The differential equation that models this situation is: (see attachment)

Answer 1

The rate of change of P with respect to t means:

dP/dt

... is directly proportional to (10-t) means:

dP/dt = k (10 - t)

where k is the constant of variation. Now also inversely proportional to cube root of P means:

dP/dt = k (10-t)/cuberoot(P)

-- Look up direct and inverse variation: http://www.purplemath.com/modules/variatn.htm