Question

At t = 0 there are 50 grams of a radioactive isotope. The isotope has a half-life of 16 minutes. Use the exponential decay model to write the amount A as a function of time t.

Answer 1

The amount of a radioactive isotope at time t can be modeled using the exponential decay function A = A0e^-kt, where A is the amount at time t, A0 is the initial amount, k is the decay constant, and t is the time in minutes. In this case, the half-life is 16 minutes.

Step-by-step explanation:

The amount of a radioactive isotope can be modeled using the exponential decay function:

A = A0e-kt

where:

• A is the amount of the isotope at time t
• A0 is the initial amount of the isotope
• k is the decay constant
• t is the time in minutes

In this case, the half-life of the isotope is 16 minutes. The decay constant k can be calculated using the formula:

k = -ln(1/2)/t1/2

Substituting the values:

• t1/2 = 16 minutes
• ln(1/2) ≈ -0.693

We can now write the amount A as a function of time t:

A(t) = 50 * e-0.693*t/16