Thread: Word Problem involving Integration

Any help as to how to get started or get through the problem will be much appreciated:

An oil spill is spreading in a circular pattern from a damaged tanker on a calm sea. The radius of the circle is growing at a rate of r'(t)=40 times the radical of t feet per minute.

A)How much does the radius grow from time t= 100 to t= 225?
B) When will the radius be 1,000 feet long?

Originally Posted by blurain

Any help as to how to get started or get through the problem will be much appreciated:

An oil spill is spreading in a circular pattern from a damaged tanker on a calm sea. The radius of the circle is growing at a rate of r'(t)=40 times the radical of t feet per minute.

A)How much does the radius grow from time t= 100 to t= 225?
B) When will the radius be 1,000 feet long?

----> use the power rule

(A) we want

or you can use the second fundamental theorem of calculus if you which, but direct integration is more fun

(B) we want and solve for t

Is r(t)=80/3 t^3/2 the correct function for the derivative r'(t)= 40 times the radical of t?

Originally Posted by blurain

Is r(t)=80/3 t^3/2 the correct function for the derivative r'(t)= 40 times the radical of t?

yes, but it should really be but we know that C = 0, so it's fine