A large stone is falling through a layer of mud and its depth x m below ground level at time t minutes is given by x = 12 - 12e^(-0.5t). How long will it take the stone to reach within 1 mm of its final position?

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- Apr 24th 2010, 06:46 AMSunyataMotion - Please, any help???
A large stone is falling through a layer of mud and its depth x m below ground level at time t minutes is given by x = 12 - 12e^(-0.5t). How long will it take the stone to reach within 1 mm of its final position?

- Apr 24th 2010, 08:01 AMsa-ri-ga-ma
- Apr 24th 2010, 08:21 AMSoroban
Hello, Sunyata!

Quote:

A large stone is falling through a layer of mud.

Its depth**m**below ground level at time minutes is given by: .

How long will it take the stone to reach within 1**mm**of its final position?

The stone reaches its final position as

. .

The final positon is 12 meters below ground level.

When will the stone be 11.99 m below ground level?

We have: .

. . . . . .

. . . . . .

Answer: about 14.2 minutes.