Question

Please help and show work ..... need fast ... college algebra The half-life for thorium-227 is 18.72 days. The amount A (in grams) of thorium-227 after t days for a 10-gram sample is given by A(t)=10⋅0.5^t/18.72 How long will it take before 1 grams of thorium-227 is left in the sample? Round your answer to the hundredths place. days

Answer 1

62.17 days

Explanation:

The computation of the number of days is shown below:

Given that

A(t)=10 × 0.5^(t ÷ 18.72)

1 = 10 × 0.5 ^ (t ÷ 18.72)

0.1 = 0.5 ^ (t ÷ 18.72)

Now consider the log in both sides

ln(0.1) = ln(0.5)^ (t ÷ 18.72)

ln(0.1) ÷ ln(0.5) = (t ÷ 18.72)

3.321928095 = (t ÷ 18.72)

So, t = 62.17 days

With the help of log, we can easily compute it