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# Lesson30 - MA 15200 Lesson 30 Exponential and Logarithmic...

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1 MA 15200 Lesson 30 Exponential and Logarithmic Application Problems In order to solve the applied problems in this lesson, a student must know how to use the log, ln, x e , and power key functions on a scientific calculator. There are lots of real life problems that have formulas with exponential or logarithmic expressions. The examples found in this lesson are just some. Ex 1: Half-Life of an Element The half-life of an element is the amount of time necessary for the element to decay to half the original amount. Uranium is an example of an element that has a half-life. The half-life of radium is approximately 1600 years. The formula used to find the amount of radioactive material present at time t , where A 0 is the initial amount present (at t = 0), and h = half-life of the element is / 00 22 t th h A A or A A  . Tritium, a radioactive isotope of hydrogen, has a half-life of 12.4 years. If an initial sample has 50 grams, how much will remain after 100 years? Round to 4 decimal places. Ex 2: Population Growth Another formula represents the population growth of lots of cities, towns, or countries. The formula is kt e P P 0 where P is the final population, P 0 is the initial population at time 0, t is time in years, and k = b - d ( b

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Lesson30 - MA 15200 Lesson 30 Exponential and Logarithmic...

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