a-balloon-is-inflated-and-its-volume-in-cubic-meters-after-ttt-seconds-is-given-

Question

A balloon is inflated, and its volume in cubic meters after tt seconds is given by the function V(t)=4tV(t)=4t. Calculate V′$$(10)V^{\prime}$$\left(10\right) and interpret the meaning of this value. Include units in your answer.

Accepted Answer

V′(10)=$$4V^{\prime}(10)=4 m3/s$$	ext{ m}^3	ext{/s}The rate of change of the volume of the balloon is 4 m3/s4	ext{ m}^3	ext{/s} at t=10t=10 s	ext{ s}.

Answer

V′(10)=$$10V^{\prime}$$\left(10ight)=10 m3/s	ext{ m}^3	ext{/s}The rate of change of the volume of the balloon is 1010 m3/s	ext{ m}^3	ext{/s} at t=10t=10 s	ext{ s}.

Answer

V′(10)=$$40V^{\prime}$$\left(10ight)=40 m3/s	ext{ m}^3	ext{/s}The rate of change of the volume of the balloon is 4040 m3/s	ext{ m}^3	ext{/s} at t=10t=10 s	ext{ s}.

Answer

V′(10)=$$5V^{\prime}$$\left(10ight)=5 m3/s	ext{ m}^3	ext{/s}The rate of change of the volume of the balloon is 55 m3/s	ext{ m}^3	ext{/s} at t=10t=10 s	ext{ s}.

A balloon is inflated, and its volume in cubic meters after tt seconds is given by the function V(t)=4tV(t)=4t. Calculate V′(10)V^{\(\prime\)}\(\left\)(10\(\right\)) and interpret the meaning of this value. Include units in your answer.

A balloon is inflated, and its volume in cubic meters after $t$ seconds is given by the function $V of t equals 4 t$ . Calculate $V prime of 10$ and interpret the meaning of this value. Include units in your answer.