Krystal Math with Dr. Kish || Calculus 1 || Exponential Growth and Decay

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Xuất bản 28/06/2016
In this video we study exponential growth and decay and solve some word problems involving phenomena that exhibit such growth or decay. In case you don't have the worksheet mentioned in the video, don't worry! Here are the 4 problems we work through: 1. The half-life for radium is approximately 1600 years. (a) Find what percentage of a given quantity of radium disintegrates in 100 years. (b) A sample of radium has a mass of 200 mg. Find a formula for the mass of radium that remains after t years. (c) When will the mass be reduced to 30 mg? 2. Every 15 minutes approximately 40% of the antibiotic ampicillin is eliminated from the body (metabolized by the liver and kidneys, for example). Say you are given a 250 mg dose. Measure time in hours. (a) What is the relative growth rate? (b) How many milligrams are left in your body after 2 hours? 3. Say a body cools from 200 degrees to 100 in 40 minutes while immersed in a medium whose temperature is 5 degrees. (a) Find a formula for T(t), the temperature T of the body (in degrees) as a function of time t (in minutes). (b) Compute the time required for the same body to cool from 100 degrees to 10. Interpret. 4. Say $3000 is invested at 5% interest. (a) How much will the investment be worth after 7 years if interest is compounded monthly? Continuously? (b) What annual interest rate would you need for the investment to double in the same amount of time? Is this realistic?
Mathematics Field Of Study Calculus Field Of Study Exponential Growth Exponential Function Radioactive Decay Compound Interest Newton's Law of Cooling
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