Activity 5 Inverse Functions and their Derivatives10. When a camera flash goes off, the batteries immediately begin to recharge the flash'scapacitor which stores electric charge given by Q(t)Q,(1-e-")where Q, is themaximum charge capacity and t is measured in secondsa. Find the inverse of this function (i.e. solve for t) and explain its meaningb. How long does it take to recharge the capacitor to 90% of capacity if a 2

Given:The function is Q(t) = Q0(1−e−t/a), where t is the time in seconds and Q0 is the maximum…

Answered: Activity 5 Inverse Functions and their…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter3: Functions And Graphs

Section3.7: Operations On Functions

Problem 52E

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Radioactive Decay The half-life of radium-226 is 1590 years. a If a sample has a mass of 150 mg, find a function that models the mass that remains after t years. b Find the mass that will remain after 1000 years. c After how many years will only 50 mg remain?
Radioactive Decay The half-life of radium-226 is 1590 years. (a)If a sample has a mass of 150 mg, find a function that models the mass that remains after tyears. (b)Find the mass that will remain after 1000 years. (c)After how many years will only 50 mg remain?
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.
Growth of North Sea Sole The length of North Sea sole, a species of fish, can be determined using the von Bertalanffy model by the formula L=14.819.1060.631t. Here t is age, in years, and L is length, in inches. a. Make a graph L versus t. Include values of t from 1 to 10 years. b. Use functional notation to express the length of a 4-year-old sole, and that calculate that value. c. At what age will a sole be 10 inches long? d. What is the limiting length for a North Sea sole?
Spawner-Recruit Model In fish management it is important to know the relationship between the abundance of the spawners also called the parent stock and the abundance of the recruitsthat is, those hatchlings surviving to maturity. According to the Ricker model, the number of recruits R as a function of the number of spawners P has the form R=APeBp for some positive constants A and B. This model describes well a phenomenon observed in some fisheries: A large spawning group can actually lead to a small group of recruits. In a study of the sockeye salmon, it was determined that A=4 and B=0.7. Here we measure P and R in thousands of salmon. a. Make a graph of R versus P for the sockeye salmon. Assume there are at most 3000 spawners. b. Find the maximum number of salmon recruits possible. c. If the number of recruits R is greater than the number of spawners P, then the difference R-P of the recruits can be removed by fishing, and next season there will once again be P spawners surviving to renew the cycle. What value of P gives the maximum value of R-P, the number of fish available for removal by fishing?

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