Exponential decay, precalc help!?

Question

Assume a model for C^14 amount of decay is
w(t) = w(0) exp(-0.000122t)
Where t is the number of Carbon 14 atoms left after t years. Assume we start with w(0) = 6 x 10^10 (the number of atoms of Carbon 14)

1. How many atoms of Carbon 14 are left aft 100,000 years? (Can someone show how to get the answer? I am confused on how to solve this!)

2. If we assume that we cannot detect reliably the amount of c^14 if there are less than 10^3 atoms, then what is oldest fossil to date?

Answer 1

(1)

w(t) = w(0) exp(-0.000122t)

Initial  amount  of Carbon 14 is w(0) = 6 x 10^10 

So w(t) = 6 x 10¹º exp(-0.000122t)

Carbon 14 are left aft 100,000 years is w(100000) = 6 x 10¹º exp(-0.000122×100000)

=6 x 10¹º exp(-12.2)

=6 x 10¹º x 0.0000050304556071

= 301827.336426

= 3.018 x 10^5

Carbon 14 are left aft 100,000 years is 3.018 x 10^5