What value does the position approach after a very long time?

Question

The position of an object is given by x(t)=4/7(1- e^-7t)

 

1.) What value does the position approach after a very long time?

2.) How long does it take to get halfway between the start position and the long term position, the horizontal asymptote?

Answer 1

Is the function

A:  x(t) = (4/7)(1 - e^-7t)
or
B:  x(t) = 4/(7(1 - e^-7t))) ?

 

In any event, here's necessary preliminary analysis that you will need.

e^-7t will approach zero as t goes to infinity.

 

Then the result for A will be 4/7, and the result for B will be 4/7 also!