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?
Hello, Sunyata!
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.