## Related questions with answers

A volcano erupts in a powerful explosion. The sound from the explosion is heard in all directions for many hundreds of kilometers. The speed of sound is about 340 meters per second.

(a) Fill in the table below showing the distance, $d$, that the sound of the explosion has traveled at time $t$. Write a formula for $d$ as a function of $t$.

Time, $t$ | $5 \mathrm{sec}$ | $10 \mathrm{sec}$ | $1 \mathrm{~min}$ | $5 \mathrm{~min}$ |
---|---|---|---|---|

Distance, $d(\mathrm{~km})$ | ||||

Area, $A\left(\mathrm{~km}^2\right)$ |

(b) How long after the explosion will a person living 200 km away hear the explosion?

(c) Fill in the table below showing the land area, $A$, over which the explosion can be heard as a function of time. Write a formula for $A$ as a function of $t$.

Time, $t$ | $5 \mathrm{sec}$ | $10 \mathrm{sec}$ | $1 \mathrm{~min}$ | $5 \mathrm{~min}$ |
---|---|---|---|---|

Distance, $d(\mathrm{~km})$ | ||||

Area, $A\left(\mathrm{~km}^2\right)$ |

(d) The average population density around the volcano is 31 people per square kilometer. Write a formula for $P$ as function of $t$, where $P$ is the number of people who have heard the explosion at time $t$.

(e) Graph the function $P=f(t)$. How long will it take until 1 million people have heard the explosion?

Solution

Verified## (a)

The distance in kilometers $(d)$ that the sound travels in time $(t)$, given in seconds, is given by

$d=0.340t$

(because $340$ m/sec = $0.340$ km/sec)

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