0.2 Exponential Decay Suppose a radioactive substance decays at a continuous rate proportional to the amount of the radioactive substance present. We can use the following formula to model the radioactive decay. Q(t) = Qo ext where Q(t) is the remaining quantity of the substance at time t, Qo is the initial quantity of the substance, and A is the decay constant. (a) If the substance has a half-life of 5 years (half-life is the time for half of the amount of material to decay) find the value of A. Show your work. (b) If the initial mass of the substance is 80 grams, how much of the substance will remain after 18 years? Show all of your work.

0.2 Exponential Decay Suppose a radioactive substance decays at a continuous rate proportional to the amount of the radioactive substance present. We can use the following formula to model the radioactive decay. Q(t) = Qo ext where Q(t) is the remaining quantity of the substance at time t, Qo is the initial quantity of the substance, and A is the decay constant. (a) If the substance has a half-life of 5 years (half-life is the time for half of the amount of material to decay) find the value of A. Show your work. (b) If the initial mass of the substance is 80 grams, how much of the substance will remain after 18 years? Show all of your work.

Algebra and Trigonometry (MindTap Course List)

4th Edition

ISBN:9781305071742

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter4: Exponential And Logarithmic Functions

Section4.CR: Chapter Review

Problem 13CC: Suppose that the initial mass of radioactive substance is m0 and the half-life of the substance is...

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Suppose that the initial mass of radioactive substance is m0 and the half-life of the substance is h. Let m(t) be the mass remaining at time t. a What is meant by the half-life h? b Write a formula for m(t) in terms of the half-life h. c Write a formula for the relative decay rate r in terms of the half-life h. d Write a formula for m(t) in terms of the relative decay rate r.
The table shows the mid-year populations (in millions) of five countries in 2015 and the projected populations (in millions) for the year 2025. (a) Find the exponential growth or decay model y=aebt or y=aebt for the population of each country by letting t=15 correspond to 2015. Use the model to predict the population of each country in 2035. (b) You can see that the populations of the United States and the United Kingdom are growing at different rates. What constant in the equation y=aebt gives the growth rate? Discuss the relationship between the different growth rates and the magnitude of the constant.
Population The table shows the mid-year populations (in millions) of five countries in 2015 and the projected populations (in millions) for the year 2025. (a) Find the exponential growth or decay model y=aebt or y=aebt for the population of each country by letting t=15 correspond to 2015. Use the model to predict the population of each country in 2035. (b) You can see that the populations of the United States and the United Kingdom are growing at different rates. What constant in the equation y=aebt gives the growth rate? Discuss the relationship between the different growth rates and the magnitude of the constant.
Radioactive Decay A sample of bismuth-210 decayed to 33 of its original mass after 8 days. a Find the half-life of this element. b Find the mass remaining after 12 days.