Solution to 7. Separation of variables become dr ue integral evaluate to: In 3y +2 = + c Apply e to get: 3y + 2 ca. Some algebra yields the general solution: y implies c4 = 26 So the particular solution is: | y 26e3a- -dr. Use 1-substitution with u 3y+2 and - dy. The integrals 1 3y + 2 l du Apply some algebra to get: In 3y +2 = 3x + c2 2 c4e3 Use IC to find C4 : 8-y(0) Exponential Growth and Mixing problems homework to be handed in. Just two problems: Problem 1. (Exponential growth) Suppose a small colony of 1,000 bacteria, at t 0 minutes is in a large bottle of water with lots of food and no predators (so there are no predation or density dependent issues to worry minutes there are 2,500 bacteria in the colony. Let y(t) = the number o in a large about). Suppose after 45 f bacteria in the colony at time t, t measured in minutes Write the ODE IVP for the above scenario and find the solution to the IVP. Use the solution to estimate how many bacteria in the bottle at t 90 minutes. Circle your answer (the number of bacteria after 90 minutes). were lem 2. (Mixing) We start with 2,000 liters of seawater in a tank. In seawater there are 35 g of salt per liter. Suppose we continually pour fresh water (0.5 g salt/liter) into the top of the tank at the rate of 10 liters/minute and at the bottom of the tank, we continually drain off 10 liters/minute. So the amount of water in the tank is always 2,000 liters. Assume that the water in the tank is being stirred so that the saltwater and the freshwater mix immediately. How long until the concent of ration salt in the tank is 6 g/liter? Circle your final answer (how many minutes until the salt concentration is 6 g/L) Instructions. On page 1, immediately after your name, write: (1) Number of bacteria after 90 min = your answer (2) Minutes until the salt concentration is 6 g/Lyo Then, underneath and on the following pages show all work. Don't skip steps. Show the integration. Use a pencil (so you can erase your mistakes). Be neat so that I can follow your work. Circle final answers. STAPLE with stapler the pages. No paper clips, etc.
Addition Rule of Probability
It simply refers to the likelihood of an event taking place whenever the occurrence of an event is uncertain. The probability of a single event can be calculated by dividing the number of successful trials of that event by the total number of trials.
Expected Value
When a large number of trials are performed for any random variable ‘X’, the predicted result is most likely the mean of all the outcomes for the random variable and it is known as expected value also known as expectation. The expected value, also known as the expectation, is denoted by: E(X).
Probability Distributions
Understanding probability is necessary to know the probability distributions. In statistics, probability is how the uncertainty of an event is measured. This event can be anything. The most common examples include tossing a coin, rolling a die, or choosing a card. Each of these events has multiple possibilities. Every such possibility is measured with the help of probability. To be more precise, the probability is used for calculating the occurrence of events that may or may not happen. Probability does not give sure results. Unless the probability of any event is 1, the different outcomes may or may not happen in real life, regardless of how less or how more their probability is.
Basic Probability
The simple definition of probability it is a chance of the occurrence of an event. It is defined in numerical form and the probability value is between 0 to 1. The probability value 0 indicates that there is no chance of that event occurring and the probability value 1 indicates that the event will occur. Sum of the probability value must be 1. The probability value is never a negative number. If it happens, then recheck the calculation.
Question 2
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 2 images
