Concept explainers
Radioactive material decays over time and the amount remaining at time
t is given by the equation
where h is the half-life of the material, which is the time it takes the
material to decay to one-half its original amount. Use this equation in
Exercises 25 and 26.
Assume that we have 50 pounds of radioactive plutonium, which
has a half-life of 24,000 years. How much plutonium will still
remain after 50,000 years?
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MATHEMATICAL IDEAS W/SUPPLEMENT & MML
- 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.arrow_forwardSuppose 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.arrow_forwardDoes the equation y=2.294e0.654t representcontinuous growth, continuous decay, or neither?Explain.arrow_forward
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