Calculus: Early Transcendentals
8th Edition
ISBN: 9781285741550
Author: James Stewart
Publisher: Cengage Learning
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Find the half-life of radioactive substance
Radium-226; A(t) = A0e-0.00043t
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- Initially, 10 grams of a radioactive substance were found in a sample. It was observed that 20% of the initial amount of radioactive substance disintegrated after 2 hours (that is, 8 grams remain after 2 hours). Find the half-life of the radioactive substance (that is, the time it takes for one- half of the initial amount to disintegrate) if the rate of disintegration of the radioactive substance is In z 1 2 0.7 proportional to the amount of the substance present at time t. You must begin your solution process by 3 considering the proportional relationship presented below. Use the natural logarithm table to the right 1.1 to provide an approximate answer. Your work must support your answer. 4 1.4 1.6 dA a A 6 1.8 dt 1.9 2.1 9 2.2 10 2.3 7,arrow_forwardSuppose a sample of 600 grams of a radioactive substance decays according to the formula Q = 600· e−0.11t where t is measured in years.Find the half-life of this substance. Round your answer to three decimal places.arrow_forwardWhich of these values for P and a will cause the function f(x)=PaX to be an exponential growth function? Which of these values for P and a will cause the function to be an exponential growth function? p=1/7;a= 1/10 P=7;a=1/10 p=7;a=1 p= 1/7 ;a=10arrow_forward
- The change to a villages population over time can be represented using an exponential decay function. P(t) = P0ert (t ≥ 0) P(t) represents the village population at time (t), measured in years. Initially at time t=0, there are 12,000 people in the village. After 4 years, only 5,000 people remain. A. Show the value of P0 is 12,000 and hence, state the equation for P(t) B. Show that the value of the constant r is −0.219 to three significant figures.C.arrow_forwardThe decay time is the time it takes for a radioactive substance to lose half of its amount. This function is given by A(t)=a e-.69*t/Twhere a is the initial amount, t is the time elapsed, T is the time it is known to decay by one-half and A(t) is the amount left. Carbon -14 has a half-life of 5,200 years. Something is assumed to be 3500 years old. How much carbon-14 is left if it is known to have started with 20 grams of carbon-14?arrow_forward
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