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Answer 25 :
Given function is,
y = ln(x+3)
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- Einsteinium-255 is a radioactive substance that decay at a continuous rate of 1.65% per day suppose we start with an initial amount of einsteinium-255, find a formula that represents the amount of einsteinium-255,N, as a function of time t.A pharmacy mixes different concentrations of saline solutions for its customers. The pharmacy has a supply of two concentrations, 0.5% and 5%. The function y=(100)(0.05)+x(0.005)/100+x gives the concentration of the saline solution after adding x milliliters of the 0.5% solution to 100 milliliters of the 5% solution. How many milliliters of the 0.5% solution must be added to the 5% solution to get a 0.95% solution?Two strains of bacteria are growing in separate Petri dishes. Initially, there are 300 Strain A bacteria and, from a prior experiment, you know that the population should double every 20 minutes. Having never worked with Strain B before, you monitor its growth over the first hour and notice that there are 200 bacteria after 30 minutes and 600 bacteria after 1 hour. 1. Let t be the number of hours that have passed since the two populations of bacteria start growing. Express the number of strain A bacteria as a function of t. Should be answered in form PA(t)=Cebt for some numers C and b. 2.The population of Strain B bascteria after t hours can be modelled by PB(t)=(200/3) 32t How many strain B bacteria were present initally. Round to nearest integer. 3. After how many hours will the two populations be equal in number? Give an exact number.
- Using ELIMINATION OF ARBITRARY CONSTANTS, find the values of c1 and c2 so that the given functions will satisfy the prescribed initial conditions.Two substances A and B are combined to form a product C. Theformation of the product is proportional to the time the reactantsare combined. The final product is composed of two parts of Bfor every part of A. If initially A is 30 kg and B is 20 kg, and 5kg of the product is formed after 30 mins., find the function ofproduct formed at any given time.Decay of Litter Litter such as leaves falls to the forest floor, where the action of insects and bacteria initiates the decay process. Let A be the amount of litter present, in grams per square meter, as a function of time t in years. If the litter falls at a constant rate of L grams per square meter per year, and if it decays at a constant proportional rate of k per year, then the limiting value of A is R=L/k. For this exercise and the next, we suppose that at time t=0, the forest floor is clear of litter. a. If D is the difference between the limiting value and A, so that D=RA, then D is an exponential function of time. Find the initial value of D in terms of R. b. The yearly decay factor for D is ek. Find a formula for D in term of R and k. Reminder:(ab)c=abc. c. Explain why A=RRekt.
- Two strains of bacteria are growing in separate Petri dishes. Initially, there are 300 Strain A bacteria and, from a prior experiment, you know that the population should double every 20 minutes. Having never worked with Strain B before, you monitor its growth over the first hour and notice that there are 200 bacteria after 30 minutes and 600 bacteria after 1 hour. Let t be the number of hours that have passed since the two populations of bacteria start growing. Express the number of strain A bacteria as a function of tt. Note: Your answer should be of the form PA(t)=Ce^(bt) PA(t)=Ce^(bt( for some numbers C and b. From your observations, you know that the population of Strain B bacteria after tt hours can be modelled by PB(t)=(200/3)3^(2t) PB(t)=(200/3)3^(2t) How many strain B bacteria were present initially? (Round your answer down to the nearest integer). After how many hours will the two populations be equal in number? Give an exact answer (no decimals).(a) If the bee is hovering at the point (0, 0, 0), what temperature is they experiencing? (b) If the bee starts at the point (0, 0, 0) and then begins moving toward an opening in the window at the point (1, 1, −1), will the temperature initially2 be increasing, decreasing, or stay the same? How do you know? (c) If the bee is hovering at the point (0, 0, 0) and wants to experience the most rapid increase in temperature, which direction should they go? (d) How quickly will the temperature change if he goes in the direction you found in part (c)?How do you draw a function that meets all these requirments? - has an average rate of change of -2 from x= -2 to x=1 - the only constant rate of change occurs from x=2 to x=5 - the only places with an instantaneous rate of change of 0 are at x=01 and x=6 - a very rapid rate of change between x= -7 and x=-5 - a very gradual rate of change when x is larger than 7 - domain: {x | x > -7, xer} - range: {y | yer}
- The molarity of a solute in solution is defined to be the number of moles of solute per liter of solution (1 mole = 6.02 × 1023 molecules). If X is the molarity of a solution of magnesium chloride (MgCl2), and Y is the molarity of a solution of ferric chloride (FeCl3), the molarity of chloride ion (Cl−) in a solution made of equal parts of the solutions of MgCl2 and FeCl3 is given by M = X + 1.5Y. Assume that X has mean 0.125 and standard deviation 0.05, and that Y has mean 0.350 and standard deviation 0.10 .Assuming X and Y to be independent, find σM.The molarity of a solute in solution is defined to be the number of moles of solute per liter of solution (1 mole = 6.02 × 1023 molecules). If X is the molarity of a solution of magnesium chloride (MgCl2), and Y is the molarity of a solution of ferric chloride (FeCl3), the molarity of chloride ion (Cl−) in a solution made of equal parts of the solutions of MgCl2 and FeCl3 is given by M = X + 1.5Y. Assume that X has mean 0.125 and standard deviation 0.05, and that Y has mean 0.350 and standard deviation 0.10. Find μM.Please let me know how to find out the answer for (b) using the substitution method. I know how to get the functions for (2) as shown. Question: A company can decide how many additional labor hours to acquire for a given week. Subcontractor workers will only work a maximum of 20 hours a week. The company must produce at least 200 units of product A, 300 units of product B, and 400 units of product C. In 1 hour of work, worker 1 can produce 15 units of product A, 10 units of product B, and 30 units of product C. Worker 2 can produce 5 units of product A, 20 units of product B, and 35 units of product C. Worker 3 can produce 20 units of product A, 15 units of product B, and 25 units of product C. Worker 1 demands a salary of $50/hr, worker 2 demands a salary of $40/hr, and worker 3 demands a salary of $45/hr. The company must choose how many hours they should contract with each worker to meet their production requirements and minimize labor cost. (a) Formulate this as a linear…