Question

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Applications of Exponential Equations Many real-life situations can be modeled by an exponential growth function of the form A(t) Ao ett constant that affects the rate of growth or decay, and t represents time. Using your knowledge of writing exponential equations that you did in the beginning of this chapter, what would A or an exponential decay function of the form A(t)-A ett where k represents the represent? 1. The amount of carbon-14 present in animal bones after t years is given by A(t) Age001 A sample of fossil had 28% of the carbon-14 of a contemporary living sample. Estimate the age of the sample. a. According to the equation, what is the constant that affects the rate of decay? b. Since we don't have an actual number for the original amount of carbon-14, we will leave that as the variable A0. If the sample currently has 28% of the carbon-14 that it started with, how can we represent that amount using the variable A? set ea c. Replace A(t) with the answer to part b. d. The question is asking for the age of the sample, so what variable are we solving for? e. Use the methods we have learned to solve exponential equations, to solve the equation. In the previous problem, the sample had 28% of the amount of carbon-14 that it had started with. If it had 50% ofthe original amount, what would we replace A(t) with? 2. a. b. In this situation, we are dealing with the half-life of a quantity. The half-life is the amount of time it takes a quantity to reach one-half of its original amount. The radioactive chemical Uranium-238 has a half life of 4.47 billion years. What is the rate of decay of this chemical? uppose there is a radioactive spill of s kg of this substance. Using the rate of decay that you found in part b above, how long will it take for the Uranium-238 to decay 3kg? Give your answer in millions of years to

Answer 1

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