Question

Set up an exponential function to model each real world situation then use it to find the requested values.

The half-life of Carbon 14 is about 5700 years. You begin with 800 grams of this isotope.

1) Function:

2) How much Carbon 14 is there after: a) 11,400 years b) 45,000 years

Answer 1

f(t) = 800(1/2)^(t/5700)
You can see that every time t increases by 5700, you have another power of 1/2, or a half-life.

So, using that, just plug in your values for t.

You can get an estimate by noting that

11400 = 2*5700
45000 ≈ 8*5700