Suppose that the price of a commodity after x years is given by f(x) = Ae^(kx) where A and k are constants.
1. Find A and k when f(0) = 4 and f0(0) = 1. In this case, what is the
price after 5 years? (Do not solve for e^x or ln(x))
2. We assume now that A = 4 and k = 0:25. When the price has increased to 18, it becomes controlled so that the annual price increases is limited to 10%. When the price controls first needed? What length of time is needed for the price to double before and after price control are introduced? (Do not solve for e^x or ln(x))
Answers
n probability theory and statistics, the exponential distribution is the probability distribution of the time between events in a Poisson point process, i.e., a process in which events occur continuously and independently at a constant average rate. It is a particular case of the gamma distribution. It is the continuous analogue of the geometric distribution, and it has the key property of being memoryless. In addition to being used for the analysis of Poisson point processes it is found in various other contexts.
The exponential distribution is not the same as the class of exponential families of distributions, which is a large class of probability distributions that includes the exponential distribution as one of its members, but also includes the normal distribution, binomial distribution, gamma distribution, Poisson, and many others.