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 ﻿ttt﻿ seconds is given by the function V(t)=4t V(t) = 4t . Calculate ﻿V′$$(10)V^{\prime}$$\left(10\right)V′(10)﻿ and interpret the meaning of this value. Include units in your answer.

Accepted Answer

﻿V′(10)=4 V'(10) = 4 V′(10)=4﻿﻿ m3/s	ext{ m}^3	ext{/s} m3/s﻿The rate of change of the volume of the balloon is ﻿4 m3/s4	ext{ m}^3	ext{/s}4 m3/s﻿ at ﻿t=10 t = 10 t=10﻿﻿ s	ext{ s} s﻿.

Answer

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

Answer

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

Answer

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

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