Question

Once again, you're trying to get out of the classroom. The distance to the door from your desk is d meters. Your first step is 1/6 that distance. Each successive step is 1/6 the previous distance. How far have you traveled? Express each result using exponetial notation for 8 steps, 12 steps, 20 steps, and n steps.

Answer 1

Given:

The distance to the door from your desk is d meters.

Your first step is 1/6 that distance =

`(1)/(6)d`

Each successive step is 1/6 the previous distance.

so, the second step =

`(1)/(6)\cdot(1)/(6)d=((1)/(6))^2d`

The third step =

`(1)/(6)\cdot((1)/(6))^2d=((1)/(6))^3d`

And so on,

So, for the step number n, the formula will be :

`=((1)/(6))^n\cdot d`

So, for 8 steps

You will have traveled =

`=((1)/(6))^8\cdot d`

For 12 steps =

`=((1)/(6))^(12)\cdot d`

For 20 steps =

`=((1)/(6))^(20)\cdot d`

For n steps =

`=((1)/(6))^n\cdot d`