Optimizing Water Flow: Finding Maximum Mass and Rate of Change

[lgen0290]

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 = 6.00t 0.8 - 3.35t + 23.00, with t 0, m in grams, and t in seconds.
(a) At what time is the water mass greatest?

(b) What is that greatest mass?

(c) In kilograms per minute, what is the rate of mass change at t = 2.00 s?

(d) In kilograms per minute, what is the rate of mass change at t = 5.00 s?

Homework Equations

The first derivative would be 4.8t^-.2-335

The Attempt at a Solution

a)I set the derivative equal to zero and figured t to be 2.3375, but it says that's wrong.
b)I assume I'd plug a into the original and try tht, but I can't get a.
c and d)I tried to put 2 and 5 into t as the original, but they are not right.

 

[blindside]

a) is, as you said, the solution for t when

\frac{dm}{dt}=0.

However, the solution to

t^{0.2}=\left[\frac{4.8}{3.35}\right]

is not 2.3375, check your algebra.

b), as you said is m(t) for the solution above
c) and d) can both be found by substituting the times into the expression for \frac{dm}{dt}.

 

[lgen0290]

Thanks. Where did the 3.35 come from? How would I solve t^-.2?

 

[blindside]

The 3.35 is from the original expression for m, unless you've mistyped it. I used logarithms and the change of base rule to solve for t.