Learning DiagnosticAnalyticsRecommendationsSkill plans4 MathCommon Core2You have prizesAlgebra 2 > T.12 Exponential growth and decay: word problems TYQ#EYou have 8,560 grams of a radioactive kind of rubidium. If its half-life is 15 minutes, howmuch will be left after 45 minutes?gramsSubmit

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College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter5: Exponential And Logarithmic Functions

Section5.2: Applications Of Exponential Functions

Problem 5E

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Use a calculator to help solve each problem. World population growth See Exercise 23. Assuming a Malthusian growth model, find the world population in 40 years. 23. World population growth The population of the Earth is approximately 6 billion people and is growing at an annual rate of 1.9%. Assuming a Malthusian growth model, find the world population in 30 years.
SKILL BUILDING EXERCISES HarvestingWhat is the name of the theory that says that a renewable resource growing logistically should be harvested at half of the carrying capacity?
Use a graphing calculator to solve each problem. In Example 4, suppose that a birth control program changed the formula for poulation growth to Pt=1000e0.01t. How long will the food supply be adequate? EXAMPLE 4 Using a Graphing Calculator to Solve a popuiation Problem Suppose that a country with a population of 1000 people is growing exponentially according to the population function Pt=1000e0.02t Where t in years. Furthermore, assume that the food supply, measured in adequate food per day per person, is growing linearly according to the function fx=30.625x+2000 In how many years will the population outstrip the food supply?
If a population decays by 60% per year, then r in an exponential growth function is . . .(a) .40 (b) .60 (c) 1.4 ( d) 1.6
American Vending Inc. (AVI) supplies vended food to a large university. Because students often kick the machines out of anger and frustration, management has a constant repair problem. The machines break down on an average of three per hour, and the breakdowns are distributed in aPoisson manner. Downtime costs the company $25 per hour per machine, and each maintenance worker gets $16 per hour. One worker can service machines at an average rate of five per hour, distributed exponentially; two workers working together can service seven per hour, distributed exponentially; and a team of three workers can do eight per hour, distributed exponentially. What is the optimal maintenance crew size for servicing the machines?
The Coronavirus can be modeled by an exponential function, but each city has a different growth rate. City A has a doubling rate every 5 days, city B has a doubling rate every 2 days. City A: number of days: 15 number of cases: 43 a. City A has a doubling rate every 5 days, how many people can we expect to be infected by day 25 if the pattern continues? b. What is the one day growth factor? c. What is the one day percent change? City B: number of days: 15 number of cases: 28 a: city B has a doubling rate every 2 days, how many people can we expect to be infected by day 25 if the pattern continues? b. What is the one day growth factor? c. What is the one day percent change?
There are currently 28 frogs in a (large) pond. The frog population grows exponentially, tripling every 6 days. How long will it take (in days) for there to be 260 frogs in the pond? Time to 260 frogs: Answer days The pond's ecosystem can support 1300 frogs. How long until the situation becomes critical? Time to 1300 frogs: Answer days
Roughly 12,000 people in a certain country are diagnosed with thyroid cancer every year, which accounts for 1% of all cancer cases. It occurs in women three times as frequently as in men. Fortunately, thyroid cancer can be treated successfully in many cases with radioactive iodine, or I-131. This unstable form of iodine has a half-life of 8 days and is given in small doses measured in millicuries. a. Suppose a patient is given an initial dose of 120 millicuries. Find the function that gives the amount of I-131 in the body after t≥0 days. b. How long does it take for the amount of I-131 to reach 25% of the initial dose? c. Finding the initial dose to give a particular patient is a critical calculation. How does the time to reach 25% of the initial dose change if the initial dose is increased by 5%?

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Learning Diagnostic Analytics Recommendations Skill plans Math Common Core You have prizes Algebra 2 > T.12 Exponential growth and decay: word problems TYQ You have 8,560 grams of a radioactive kind of rubidium. If its half-life is 15 minutes, how much will be left after 45 minutes? grams Submit