This is an exponential function and can be expressed as:
f=ir^t, f=final amount, i=initial amount, r=common ratio or "rate", t=time common ratio is applied or "time".
In this case: i=35000, r=(100-3.5)/100=0.965, so the exponential decay function is:
f=35000(0.965)^t
You can graph this with any graphing calculator or even if you type in most browser bars "y=35000(0.965^x)"
But mathematically:
15000>35000(0.965)^t divide both sides by 35000
3/7>0.965^t take the natural log of both sides
ln(3/7)>t ln(0.965) dividing both sides by ln(0.965), and remembering to reverse inequality sign because of division/multiplication by a negative value
t>ln(3/7)/ln(0.965)
t>23.78
So the population will drop below 15000 during the 23rd year.
