dt. Next, we integrate both sides.
∫ = ∫^ k dt
ln V = kt + C 0
V = Cekt
Next, we plug in V = 36π and t = 0 to solve for C: 36π = Ce^0 so C = 36π. This gives us the
equation V = 36πekt. Next, we plug in V = 90π and t = 1 to solve for k: 90π = 36πek.
k = ln ≈ 0.916
Therefore, the equation for the volume of the sphere, V, at time t is V ≈ 36πe0.916t, or if we
want an exact solution, it is V = 36π . Finally, we can solve for the volume at time t = 3: V ≈
36 πe0.916(3) ≈ 1,766ft^3 or V = ft^3 . (And, if we are concerned with significant figures, the
volume can be written as 1,800.)
7.
