Question

Lead-210 decays according to the exponential function y yo e -0.0321What is the half-life of Lead-210?Choose the correct answer below.OA. Solve 0.75% Yo1OB. Solve Yo Yo-0.0321-0.0321OC. Evaluate y=100 e -0.032(32)D. Evaluate y=100e -0.032(16)where t is time in years. Match the given question with the correct procedure to answer the question.

Answer 1

Given:

$y=y_0e^{-0.0321t}$

Where the function represents the exponential decay of lead-210.

Let's find the half-life of lead-210.

Since this is an exponential decay function, we have:

y = final amount after a given time

y₀ is the initial amount

t is the time.

Now, to find the half-life, we have:

The half-life is the time that is required to half the initial amount of the substance.

Since the initial amount is y₀, the half will be:

$\frac{1}{2}y_0$

Therefore, the correct procedure to find the half-life is:

$\frac{1}{2}y_o=y_oe^{-0.0321t}$

ANSWER: B

$\frac{1}{2}y_o=y_0e^{-0.0321t}$