A radioactive isotope has a half-life of 10 minutes.
At the start of an experiment, the activity of a sample of this isotope was 800 counts
per second after allowing for background radiation.
Calculate how long it would be before the activity fell from 800 counts per second to
200 counts per second.

The time for activity to fell from 800 counts per second to 200 counts per second is 20 minutes

Explanation:

Expression for rate law for first order kinetics is given by:

where,

k = rate constant

t = age of sample

a = let initial amount of the reactant

a - x = amount left after decay process  

a) for finding the rate constant:

Half life is the amount of time taken by a radioactive material to decay to half of its original value.

b) for activity to fell from 800 counts per second to 200 counts per second.

The time for activity to fell from 800 counts per second to 200 counts per second is 20 minutes

i don't see a text, but i am gonna assume this *orbit* the curved path, usually elliptical, described by a planet, satellite, spaceship, etc., around a celestial body, as the sun.