Suppose researchers marked 800 turtles and later were able to trap a total of 300 individuals in that population, of which 150 were marked. what is the estimate for total population size

The estimate for the total population size is 1600.

Setting up a proportion for this, we know that 150 out of our 300 turtle sample is marked; this is the first ratio for the proportion.  We also know that we marked 800 of our total population, which we will call x:

150/300 = 800/x

Cross multiply:
150*x = 300*800
150x = 240000

Divide both sides by 150:
150x/150 = 240000/150
x = 1600