Intro to Exponential Decay
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- (Video) Exponential Decay and Finding Half-Life by PatrickJMT Here's a video by PatrickJMT showing you a typical exponential decay problem involving half-life. Summary\large{\te…
By Alex Federspiel, Amy Feraco, Anusha Rahman
- An exponential function is a function whose rate of growth is controlled by the independent variable. The general form of an exponential function is: y=abxy=ab^xy=abx where bbb …
By Liza Sulkin, Victor Wang, Anusha Rahman
- Expiinium\color{purple}{\text{Expiinium}}Expiinium === How to calculate rate of decay, half life, and more!\text{How to calculate rate of decay, half life, and more!}How to calc…
By Liza Sulkin, Anusha Rahman
- Exponential Decay We see exponential decay in a lot of aspects of life, including radioactive decay. The formula to calculate exponential decay is: y(t)=y0e(−λt)y(t)=y_0e^(- \la…
By Anusha Rahman
Problems 24
- Josh purchased a laptop worth 5000\50005000 in the year 201020102010. It loses its value by 6%6\%6% per year. What is the value of the music system in 201620162016? Round to the…
- In 200820082008, Cooper bought a car for 36000\3600036000. It depreciates 12%12\%12% per year. What year will the car be worth 6000\60006000?
- The half-life of an isotope is 333 years. how many years would it take a 101010 mg sample to decay to 0.50.50.5 mg? Round to the nearest year.
- An isotope has a half-life of 252525 years. If 222 grams of the isotope disintegrates over 100100100 years, how much would remain?
- A chess tournament starts with 128128128 participants. After each round, half of them leave. How many are left after 666 rounds?
- If 400400400 mg of ibuprofen decreases about 30%30\%30% every hour, how long would it take for 424242 mg to remain?
- An isotope decays exponentially. Suppose that after one minute, there are 101010 grams remaining, and after five minutes, there are 222 grams remaining. What is the half-life, i…
- You drop a ball from a 101010-meter high platform. On the first bounce, it rises to a height of 555 meters, and every time it bounces, it loses half of its height. On which boun…
- Exponential functions of the form f(x)=P0ektf(x)=P_{0}e^{kt}f(x)=P0ekt exhibit exponential decay for which values of kkk?
- An isotope has a half-life of 666 hours. (Note: half-life is the time it takes for half of a substance to decay.) If we start with a 100010001000 milligram sample of the isotope…
- An isotope has a half-life of 121212 hours. (Note: half-life is the time it takes for half of a substance to decay.) If we start with a 404040 milligram sample of the isotope, h…
- An isotope has a half-life of 333 days. (Note: half-life is the time it takes for half of a substance to decay.) If we start with a 200200200 milligram sample of the isotope, ho…
- Which of the following functions model exponential decay? (Select all that apply)
- Exponential functions of the form f(x)=P0axf(x)=P_{0}a^{x}f(x)=P0ax exhibit exponential decay for which values of aaa?
- Which of the following functions model exponential decay? (Select all that apply)
- Imagine you're waiting in line for ice cream and you're the very last person in line. You notice that the number of people in line decreases by 30%30\%30% every minute. If there…
- A participant in a hot-dog eating contest is able to eat hot-dogs exponentially fast! If he initially has 505050 hot-dogs and 101010 minutes later, only has 101010 more to go, b…
- A snowman is melting exponentially as the temperature rises. At first, he was 222 meters tall. After 111 hour in the sun, he had melted to a mere 0.50.50.5 meters. What is the r…
- You're driving a car, going 606060 miles per hour (216,000216,000216,000 miles per second), when you notice that the speed limit is reduced to 353535 mph (126,000126,000126,000 …
- You're driving a car, going 505050 miles per hour (180,000180,000180,000 miles per second), when you notice that the speed limit is reduced to 252525 mph (90,00090,00090,000 mil…
- Suppose that each repetition succeeds with probability 99.999%99.999\%99.999%, independent of the success or failure of all other repetitions. What is the probability that the m…
- You drop a ball from a xxx-meter high platform. On the first bounce, it rises to a height of x2\frac{x}{2}2x meters, and every time it bounces, it loses half of its height. On …
- You drop a ball from a 101010-meter high platform. Every time it bounces, it loses 1x\frac{1}{x}x1 of its height. On which bounce does the ball reach a height of 101010 centime…
- You drop a ball from a 101010-meter high platform. Every time it bounces, it loses a third of its height. On which bounce does the ball first fail to reach a height of 101010 ce…