Exponential Decay
Exponential decay is a fundamental concept in mathematics and science, describing the gradual decrease of a quantity over time in a manner proportional to its current value. It is characterized by a rapid initial decline followed by a continuous slowing down as the quantity approaches zero. This phenomenon finds application in various fields, including physics, chemistry, biology, and economics. Understanding exponential decay is crucial for predicting the behavior of systems undergoing natural degradation or decay processes, as well as for designing strategies to mitigate such effects or harness them for practical purposes.
Questions
- How do you determine whether each function represents exponential growth or decay #y=10(3.5)^x#?
- Is the function # y = -5(1/3)^ -x# exponential growth or decay?
- Is the equation #A=21000(1-.12)^t# a model of exponential growth or exponential decay, and what is the rate (percent) of change per time period?
- What is the exponential decay formula?
- What is the difference between the graph of a exponential growth function and an exponential decay function?
- One job can be finished by 30 workers for 60 days. The work was started by 20 workers, and after 10 days came 5 workers. For how long will the whole work be done?
- What is the ending balance of $210 invested at 8% for 7 years?
- You are biking at a speed of 18 miles per hour. You are 3 miles behind your friend, who is biking at a speed of 12 miles per hour. What is the equation to calculate how long it will take for you to catch up to your friend?
- How do you create an (x,y) table for #y=\frac{3}{4} \cdot 6^{-x}#?
- Colleen's station wagon is depreciating at a rate of 9% per year. She paid $24,500 for it in 2002. What will the car be worth in 2008 to the nearest hundred dollars?
- How do you know if #y = 2.5(0.8)^x# represents exponential growth or decay?
- Due to melting, an ice sculpture loses one-half its weight every hour. After 8 hours, it weighs #5/16# of a pound. How much did it weigh in the beginning?
- The value of a car decreases at an annual rate of 9.9%. It is currently worth $15000. When will the car be worth $100?
- I am not sure I am posting this in the right section, but I need to determine the amount of carbon will be in 5670 years. See picture. Thanks?!!
- How do you determine whether each function represents exponential growth or decay #y=3(5/2)^x#?
- How do you determine whether each function represents exponential growth or decay #y=(0.5)^x#?
- If $12000 is invested at 4% compound quarterly, what is the amount after 8 years?
- How do you graph #y=(\frac{1}{5})^x#?
- A club has 5,000 members at the end of its first year. Each year 10% of members leave and 100 new members join. Write recursive equation for the number of members after #n# years. How many members are there at the end of the #4^(th)# year?
- A certain company loses $157,500 during a 10 month period. What is the average monthly loss?