EXPONENTIAL AND LOGARITHMIC FUNCTIONS Finding the final amount in a word problem on continuouse expo... The mass of a radioactive substance follows a continuous exponential decay model. A sample of this radioactive substance has an initia mass of 3817 kg and decreases continuously at a relative rate of 15% per day. Find the mass of the sample after three days. Do not round any intermediate computations, and round your answer to the nearest tenth. kg ? X

EXPONENTIAL AND LOGARITHMIC FUNCTIONS Finding the final amount in a word problem on continuouse expo... The mass of a radioactive substance follows a continuous exponential decay model. A sample of this radioactive substance has an initia mass of 3817 kg and decreases continuously at a relative rate of 15% per day. Find the mass of the sample after three days. Do not round any intermediate computations, and round your answer to the nearest tenth. kg ? X

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Description: See attachment EXPONENTIAL AND LOGARITHMIC FUNCTIONSFinding the final amount in a word problem on continuouse expo...The mass of a radioactive substance follows a continuous exponential decay model. A sample of this radioactive substance has an initi

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter5: Inverse, Exponential, And Logarithmic Functions

Section5.3: The Natural Exponential Function

Problem 25E

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Suppose that the initial size of a population is n0 and the population grows exponentially. Let n(t) be the size of the population at time t. (a) Write a formula for n(t) in terms of the doubling time a. (b) Write a formula for n(t) in terms of the relative growth rate r.
Bacteria Decay A lab culture initially contains 500 bacteria. Two hours later, the number of bacteria decreases to 200. Find the exponential decay model of the form B=B0akt that approximates the number of bacteria B in the culture after t hours.
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More on the Pacific Sardine This is a continuation of Example 5.1. In this exercise, we explore the Pacific sardine population further, using the model in Example 5.1. a. If the current level of the Pacific sardine population is 50,000 tons, how long will it take for the population to recover to the optimum growth level of 1.2milliontons? Suggestion: One way to solve this is to make a new logistic formula using K2.4, r0.338, and N(0)0.05. b. The value of r used in Example 5.1 ignores the effects of fishing. If fishing mortality is taken into account, then r drops to 0.215 per year with the carrying capacity still at 2.4milliontons. Answer the question in part a using this lower value of r. Note: The population estimate of 50,000 tons and the adjusted value of r are given in the paper by Murphy see footnote 3 on page 347. Murphy points out that factoring in the growth of the competing anchovy population makes the recovery times even longer, and he adds. "It is disconcerting to realize how slowly the population will recover to its level of maximum productivity ... even if fishing stops." Studies to fit a logistic model to the Pacific sardine population have yielded. N=241+239e0.338t where t is measured in years and N is measured in millions of tons of fish. Part 1 What is r for the Pacific sardine? Part 2 According to the logistic model, in the absence of limiting factors, what would be the annual percentage growth rate for the Pacific sardine? Part 3 What is the environmental carrying capacity K? Part 4 What is the optimum yield level? Part 5 Make a graph of N versus t. Part 6 At what time t should the population he harvested? Part 7 What portion of the graph is concave up? What portion is concave down?
A Skydiver If a skydiver jumps from an airplane, his velocity v, in feet per second, starts at 0 and increases towards terminal velocity, an average-sized man has a terminal T of about 176 feet per second. The difference D=Tv is an exponential function of time, a. What is the initial value of D? b. Two second into fall, the velocity is 54.75 feet per seconds. Find an exponential formula for D. c. Find a formula for v. d. Express the velocity 4 seconds into the fall using functional notation, and then calculate that value.