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## Homework Statement

Water is poured into a container that has a leak. The mass

*m*of the water is given as a function of time

*t*by

*m*= 4.9

*t*- 3.0

^{.8}*t*+ 21, with

*t*≥ 0,

*m*in grams, and

*t*in seconds.

**(a)**At what time is the water mass greatest, and

**(b)**what is that greatest mass? What is the rate of mass change at

**(c)**

*t*= 2.4 s and

**(d)**

*t*= 5.4 s?

I know that part c and d have to kg/min

## Homework Equations

m=4.9t

^{.8}-3.0t+21

d/dm =3.92t

^{-.2}-3.0

## The Attempt at a Solution

I got part

**(a)**correct as 3.80911 by finding the points of inflection from the derivatives and then looking at where the equation changes from positive to negative. Part

**(b)**was also easy because all I had to do is plug my answer into the original equation and I got 23.8568361. It's part

**(c)**and

**(d)**that I'm having trouble with.

For part

**(c)**and

**(d)**I know I have to take the derivative so I did and got

3.92t

^{-.2}- 3.0 then I plug in

3.92(2.4)

^{-.2}- 3.0=.2903630437g and 3.92(5.4)^(-.2) - 3.0= -.2022602387g