# Math Help - geometric sequence problem

1. ## geometric sequence problem

Hello

Here's the question I need a hand with:

When satellites are put into orbit, they travel around the globe, relying on the earth's gravitational pull to slingshot it around. Scientists discovered that every 100 orbits the satellite does, its distance is 98% of what it was previously. They have also discovered that when the satellite is 50% of its original distance, the gravitational pull would be too much and it will fall to the surface of the planet.
If each orbit of the earth lasts for 7 days:

Find how many orbits it would take for the satellite to be 75% of it's original distance from the earth (answer to the nearest one orbit)

Also, find how long a satellite will last in orbit (answer to the nearest day)

2. let $n$ = number of orbits
$R_0$ = initial orbital radius
$R$ = orbital radius for any number of orbits $n$
$R = R_0 (.98)^{100n}$
determine the number of orbits it takes for $\frac{R}{R_0} = .75$