Related rates problem

Question

The rate at which ice is melting in a pond is given by dV/dt= √(1+2^t), where V is the volume of ice in cubic feet, and t is the time in minutes. What amount of ice has melted in the first 5 minutes? 

 

Could someone please tell me how to do this problem? I tried doing the derivative and then plugging in 5 but I did not get the right answer. 

Answer 1

Rewrite the given fact as dV = sqrt(1+2^t)dt; they want a volume so let's do this definite integral for t = 0 up to t = 5:
∫sqrt(1+2t)dt = 14.53 cubic feet (using calculator to evaluate the def. integral.