Volume of water in barrel

Question

for time t is equal to or greater than 1 hours the volume of water in barrel is 

v(t) = 50-20/t²

how much water is in barrel at t=2 hours? 

Compute lim t--> infinity 

what Does this mean? 

 

Answer 1

Hello Zack, for the first part, we need to substitute t=2 into your equation  v(t) = 50-20/t²

 

v(t) = 50-20/2 = 50-10 = 40 (i don't know what units Volume should be in)

 

To compute the limit, think about how the equation changes as time approaches infinity (i.e. after a long time).

As t gets larger and larger, the term 20/t² gets smaller and smaller since it approaches zero. As a result, 

we are subtracting a smaller number from 50. 

Eventually, we will be subtracting 0 from 50. Therefore, the solution would be V(t→∞) = 50 - 0 = 50

 

A trick for these problems is to substitute t= ∞ and if you are dividing by ∞,then the term becomes 0. This is how I got 20/t² = 20/∞² = 20/∞ = 0.

 

Let me know if this helps!