Problema Solution
1) Do this problem without using the exponential model:
A(t) = A sub(0) e^kt
Initially there are 400 grams of a radioactive substance on hand. If the half-life of the substance is 8 hours, give an educated guess of how much remains (approximately) after 17 hours. After 23 hours. After 33 hours.
2) Construct an exponential model A(t) = A sub(0) e^kt for the amount remaining of the decaying substance in Problem 1. Compare the predicted values A(17), A(23), and A(33) with your guesses.
Here is my solution for the first problem:
17 hours ---- 400^1/4 = approximately 100 g
23 hours ---- 400^1/8 = approximately 50 g
33 hours ---- 400^1/16 = approximately 25 g
I need help with the second problem.
Answer provided by our tutors
To solve for these quantities using the exponential formula, we use:
A(t) = 400(1.-0.5)^t
where 't' is expressed as the half-life value of 8, so
after 17 hrs, t = 17 / 8 = 2.125
after 23 hrs, t = 23 / 8 = 2.875
after 33 hrs, t = 33 / 8 = 4.125
the formula then gives these amounts:
after 17 hrs, 91.7g remains
after 23 hrs, 54.5g remains
after 33 hrs, 22.9g remains