Exponential Growth and Decay
Exponential growth and decay are fundamental concepts in mathematics and various scientific disciplines, describing dynamic processes where quantities change at a rate proportional to their current size. In the context of growth, such as population expansion or compound interest, exponential functions exhibit rapid and accelerating increases over time. Conversely, decay models the gradual decrease in quantities like radioactive substances or the depreciation of assets. Understanding these phenomena is crucial in fields like finance, biology, and physics, enabling predictions and analyses essential for decision-making and problem-solving in diverse real-world scenarios.
Questions
- How do you write an exponential function whose graph passes through the points (0,-18) and (-2,-2)?
- How do you tell whether #f(x)=(6/5)^x# is an exponential growth or decay?
- How do you find the equation of the exponential function #y=a(b)^x# which goes through the points(2, 18) and (6,91.125). What is the intercepts of this function?
- Radium-221 has a half-life of 30 seconds. How long will it take for 94% of a sample to decay?
- How do you find the exponential function f(x)= a^x whose graph goes through the point (3, 1/125)?
- If 2^x = 3, what does 4^(-x) equal?
- How do you find the y-intercept of #y=10(4^x)#?
- The number of bacteria in a culture initially and after 10 hours can be given by the points (0, 250) and (10, 540), where x is the number of hours and y is the number of bacteria. Use the 2 points to write the model y=ae^bx. How Do I Solve This Problem?
- How is exponential decay related to a half-life?
- How do I find the multiplier for a rate of exponential decay?
- How to find an equation of exponential decay?
- What happens when something grows exponentially?
- How long does it take the culture to double its mass if a bacterial culture which is growing exponentially increases from 5 g to 7 g in 11 hours?
- Joe Smith invest his inheritance of $50,000 in an account paying 6.5% interest. If interest is compounded continuously, how long will it take for the account to be $200,000?
- How do you simplify #64^pidiv2^pi#?
- How do you write an exponential equation that passes through (0, -2) and (2, -50)?
- How do you write an exponential equation that passes through (-1, .5) and (2, 10)?
- How do I find an exponential growth function in terms of #t#?
- Is #y = -3^x# an exponential function?
- How do you write an exponential equation that passes through (0,3) and (2,6)?