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LO 4.1 Exponential Functions 277 93. Maximum Growth Rate. The rate of growth of the fungus Fusarium verticilloides is F(t) = e -(9/(t-15)+0.56/(35-t)) where t is the temperature in degrees Celsius and 15

LO 4.1 Exponential Functions 277 93. Maximum Growth Rate. The rate of growth of the fungus Fusarium verticilloides is F(t) = e -(9/(t-15)+0.56/(35-t)) where t is the temperature in degrees Celsius and 15

College Algebra
College Algebra
1st Edition
ISBN:9781938168383
Author:Jay Abramson
Publisher:Jay Abramson
Chapter6: Exponential And Logarithmic Functions
Section6.1: Exponential Functions
Problem 61SE: The fox population in a certain region has an annualgrowth rate of 9 per year. In the year 2012,...
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LO 4.1 Exponential Functions 277 93. Maximum Growth Rate. The rate of growth of the fungus Fusarium verticilloides is F(t) = e -(9/(t-15)+0.56/(35-t)) where t is the temperature in degrees Celsius and 15<t<35.3 a) Compute lim, F(t). t-15 b) Compute lim F(t). t-35 Maximize the function F(t) for 15 <t< 35. Use parts (a) and (b) to verify that you found a maximum. 94. Maximum Growth Rate. The rate of growth of the fungus Fusarium graminearum is proportional to F(t)=e-(9/(-15)+0.69/(31-1)) where t is the temperature in degrees Celsius and 15<t< 31.4 a) Compute lim F(t). 1-15+ b) Compute lim F(t). t-31- c) Maximize the function F(t) for 15 <t< 31. Use parts (a) and (b) to verify that you found a maximum. (Death Rate. The annual death rate (per thousand) in Mexico may be modeled by the function 30.48 D(t) = 34.4- 1+ 29.44e -0.072t where t is the number of years after 1900.5 95 a) According to this model, what will Mexico's death rate be in 2010? in 2050? b) Find and interpret lim D(t). (96.) a) Find D'(t) and interpret its meaning. b) Between 2007 and 2008, by how much will Mexico's death rate decline? t-x 97. Use Newton's method to solve the equation 5 = 3.2e1.07x 98. Use Newton's method to solve the equation 2e0.041 = 6.3t. 99. Capture Probability. The probability that a tadpole with mass 0.1 g is captured by notonectids (aquatic insects) in an experiment is Deaths per 1000 population 20 1 P = 1- 1+e -(0.055+0.083T) T 40 60 Years since 1900 80 100 where T is the water temperature in degrees Celsius. Suppose that when the water temperature is 20°C, it is rising at the rate of 2 degrees per hour. How fast is the probability of capture decreasing?6 100. Capture Probability. In an experiment where the water temperature is 25°C, the probability that a tadpole is captured by notonectids (aquatic insects) is 1 P=1- 1+e -5.297+31.669m 34Stewart, Reid, Nicol, and Schaafsma, "A mathematical simulation of growth of Fusarium in Maize ears after artificial inoculation," Analytical and Theoretical Plant Pathology, Vol. 92, No. 5, pp. 534-541 (2002). $B.J.L. Berry, L. S. Hall, R. Hernandez-Guerrero, and P. H. Martin, "Mexico's Demographic Transition: Public Policy and Spatial Process," Population and Environment, Vol. 21, 363-383 (2000). where m is the tadpole's mass in grams. Suppose that when the tadpole has a mass of 0.2 g, it is growing at a rate of 0.1 g/wk. How fast is the probability of capture increasing?7 6.7 Anderson, Kiesecker, Chivers, and Blaustein, "The direct and indirect effects of temperature on a predator-prey relation- ship," Can. J. Zool, Vol 79, pp. 1834-1841 (2001). €
Transcribed Image Text:LO 4.1 Exponential Functions 277 93. Maximum Growth Rate. The rate of growth of the fungus Fusarium verticilloides is F(t) = e -(9/(t-15)+0.56/(35-t)) where t is the temperature in degrees Celsius and 15<t<35.3 a) Compute lim, F(t). t-15 b) Compute lim F(t). t-35 Maximize the function F(t) for 15 <t< 35. Use parts (a) and (b) to verify that you found a maximum. 94. Maximum Growth Rate. The rate of growth of the fungus Fusarium graminearum is proportional to F(t)=e-(9/(-15)+0.69/(31-1)) where t is the temperature in degrees Celsius and 15<t< 31.4 a) Compute lim F(t). 1-15+ b) Compute lim F(t). t-31- c) Maximize the function F(t) for 15 <t< 31. Use parts (a) and (b) to verify that you found a maximum. (Death Rate. The annual death rate (per thousand) in Mexico may be modeled by the function 30.48 D(t) = 34.4- 1+ 29.44e -0.072t where t is the number of years after 1900.5 95 a) According to this model, what will Mexico's death rate be in 2010? in 2050? b) Find and interpret lim D(t). (96.) a) Find D'(t) and interpret its meaning. b) Between 2007 and 2008, by how much will Mexico's death rate decline? t-x 97. Use Newton's method to solve the equation 5 = 3.2e1.07x 98. Use Newton's method to solve the equation 2e0.041 = 6.3t. 99. Capture Probability. The probability that a tadpole with mass 0.1 g is captured by notonectids (aquatic insects) in an experiment is Deaths per 1000 population 20 1 P = 1- 1+e -(0.055+0.083T) T 40 60 Years since 1900 80 100 where T is the water temperature in degrees Celsius. Suppose that when the water temperature is 20°C, it is rising at the rate of 2 degrees per hour. How fast is the probability of capture decreasing?6 100. Capture Probability. In an experiment where the water temperature is 25°C, the probability that a tadpole is captured by notonectids (aquatic insects) is 1 P=1- 1+e -5.297+31.669m 34Stewart, Reid, Nicol, and Schaafsma, "A mathematical simulation of growth of Fusarium in Maize ears after artificial inoculation," Analytical and Theoretical Plant Pathology, Vol. 92, No. 5, pp. 534-541 (2002). $B.J.L. Berry, L. S. Hall, R. Hernandez-Guerrero, and P. H. Martin, "Mexico's Demographic Transition: Public Policy and Spatial Process," Population and Environment, Vol. 21, 363-383 (2000). where m is the tadpole's mass in grams. Suppose that when the tadpole has a mass of 0.2 g, it is growing at a rate of 0.1 g/wk. How fast is the probability of capture increasing?7 6.7 Anderson, Kiesecker, Chivers, and Blaustein, "The direct and indirect effects of temperature on a predator-prey relation- ship," Can. J. Zool, Vol 79, pp. 1834-1841 (2001). €
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