Question

oil is leaking out of a ruptured tanker at the rate of r(t) = 50e^(-0.05t) thousand liters per minute.

How many thousands of liters leak out during the first hour?

Answer 1

Looks like you have to integrate. Are you taking calculus? If so, you would integrate from time equals 0 to time equals 60 minutes.

Answer 2

Really the equation is saying this:
dV/dt = 50*e^(-0.05t)
Where v is volume.
This can be rewritten as
dV = 50*e^(-0.05t)dt
Now you can integrate both sides. The left side will just turn into a V.

Answer 3

Remember also that [d/dx(e^(ax))] = [a*e^(ax)]
So, if you integrate [e^(ax)], you get [e^(ax)/a]