Question

Plutonium -249 decays according to the function q(t) = q0e -kt where q represents the quantity remaining after t years and k is the decay constant, .00011... to the nearest 10 years, how long will it take 24 grams of plutonium -249 to decay to 20 grams?

Answer 1

Using the decay function q(t) = q0e^-kt, it can be calculated that it will take approximately 150 years to the nearest 10 years for 24 grams of plutonium-249 to decay to 20 grams.

Step-by-step explanation:

To determine how long it will take for 24 grams of plutonium-249 to decay to 20 grams, we use the decay function q(t) = q0e-kt, where q is the quantity remaining after t years, q0 is the initial quantity, and k is the decay constant. Given that the decay constant k is 0.00011, we can set up the equation as follows: 20 = 24e-(0.00011)t.

First, divide both sides by 24 to isolate the exponential expression:

20/24 = e-(0.00011)t

Next, take the natural logarithm of both sides to solve for t:

ln(20/24) = -(0.00011)t

t = ln(20/24) / -0.00011

Calculating this, we find that t is approximately 152.14 years, so to the nearest 10 years, it would take about 150 years for 24 grams of plutonium-249 to decay to 20 grams.