Question

A sample of 700 g of lead-210 decays to polonium-210 according to the function given by A(t) = 700-0.032, where t is time in years. What is the amount of the sample after 40 years (to the nearest g)?

Answer 1

After 40 years, approximately 194 grams of lead-210 will remain, following the corrected exponential decay function A(t) = 700e^-0.032t.

Step-by-step explanation:

The question concerns the radioactive decay of lead-210 to polonium-210. There seems to be a typo in the provided function. Assuming the correct function for the decay is A(t) = 700e-0.032t, where A(t) is the amount remaining after time t in years, we can calculate the amount remaining after 40 years. Using this function:

A(40) = 700e-0.032(40)

A(40) = 700e-1.28

A(40) ≈ 700 × 0.2776 (using a scientific calculator)

A(40) ≈ 194.32 g

To the nearest gram, approximately 194 g of lead-210 will remain after 40 years.