Air Purification During testing of a certain brand of air purifier, the amount of smoke remaining (as a percent of the original amount) t min after the start of the test was given by the following function. A(t) = -0.00006+5 +0.00468t40.1438t3+1.9172 - 17.63t+ 90 Compute the following values. A'(10) = A"(10) =

Air Purification During testing of a certain brand of air purifier, the amount of smoke remaining (as a percent of the original amount) t min after the start of the test was given by the following function. A(t) = -0.00006+5 +0.00468t40.1438t3+1.9172 - 17.63t+ 90 Compute the following values. A'(10) = A"(10) =

Big Ideas Math A Bridge To Success Algebra 1: Student Edition 2015

1st Edition

ISBN:9781680331141

Author:HOUGHTON MIFFLIN HARCOURT

Publisher:HOUGHTON MIFFLIN HARCOURT

Chapter8: Graphing Quadratic Functions

Section: Chapter Questions

Problem 17CT

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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.
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Continued This is a continuation of Exercise 13. As we saw earlier, the stock turnover rate of an item is the number of times that the average inventory of the item needs to be replaced as a result of sales in a given time period. Suppose that a hardware store sells 80 shovels each year. a. Suppose that the hardware store maintains an average inventory of 5 shovels. What is the annual stock turnover rate for the shovels? How is this related to the yearly number of orders to the wholesaler needed to restock inventory? b. What would he the annual stock turnover rate if the store maintained an average inventory of 20 shovels? c. Write a formula expressing the annual stock turnover rate as a function of the average inventory of shovels, identify the function and the variable, and state the units.