Study figure 10-3. how much nitrogen-14 will be produced from a 200-g sample of carbon 14 after 17,190 years

For this problem, we use the formula for radioactive decay which is expressed as follows:

An = Aoe^-kt

where An is the amount left after time t, Ao is the initial amount and k is a constant. 

We calculate as follows:

An = Aoe^-kt
0.5 = e^-k(5730)
k = 1.21x10^-4

An = Aoe^-kt
An = 200e^-1.21x10^-4(17190)
An = 25

Therefore, about 175g is produced.