University:
Santa Ana College
Course:
MATH 150 | Calculus for Biological, Management and Social Sciences
Academic year:

2023
Views:

168

Pages:

3
Author:

guardiafamilynzfg

Logarithmic and Exponential Function Applications Math 150 Name:_______________________ 1) A research assistant in biology finds in an experiment that at low temperatures the growth of a certain bacteria can be modeled by: f (t ) = 750 + 12Lnt t ≥1 Where t represents the number of hours since the start of the experiment and f(t) represents the number of bacteria present. € a) Determine f '(t) b) Evaluate and interpret f(12) and f ’(12) € 2) Prescription drug companies of the new drug Vectrum have found that the popularity of the new drug has dwindled and can be modeled by: f (x ) = 150 + 5Lnx x ≥1 Where x represents the number of years the drug has been on the market and f(x) represents the number of prescriptions written for the drug annually in thousands. € a) Determine f '(t) b) Evaluate f ’(2) and f ’(10) and interpret each. € 3) The life expectancy for African-American females in the United States can be modeled by: f (x ) = 68.41 + 1.75Lnx 1 ≤ x ≤ 26 Where x represents the birth year since 1969 and f(x) represents the life expectancy in years. (Source: U.S. National Health Center for Health Statistics) € a) Determine f ‘(x) b) Evaluate and Interpret f(3) and f ‘(3) 4) A veterinarian finds that when a lab animal specimen is exposed to a new pesticide, the growth of a tumor in the specimen can be modeled by: f (t ) = 2.1 e 0.2t t >0 Where t represents the number of days since exposure to the pesticide and f(t) represents the diameter of the tumor in millimeters. € a) Determine f ‘(t) b) Evaluate and Interpret f ‘(3) 5) The average salary of players in the National basketball Association (NBA) can be 1 ≤ x ≤ 14 modeled by: f (x) = 280.8e 0.16x Where x represents the number of years since 1984, and f(x) represents the average salary in thousands of dollars. (Source: U.S. Statistical Abstract) € € a) Determine f ‘(x) b) Evaluate and Interpret f ‘(3) and compare to f ‘(13) 6) A manufacturer can produce VCRs at a cost of $125 apiece and estimates if the are sold for x dollars apiece, consumers will buy 1000e−0.02x each week. a) Express the Profit as a function of x (remember x is the price!) € b) At what price should manufacturers sell the VCRs to maximize profit? € € € € € € € € € Answers: 12 b) 12 hours after the start of the experiment there are about 780 bacteria and t the number is growing at a rate of about 1 bacteria/hour. 5 2) a. b. the rate of growth after 2 years is about 2.5 thousand prescriptions/year x € while the growth rate after 10 years is .5 thousand prescriptions/year. (or 2500/year and 500/year) 1) a. € 1.75 b. In 1972 the life expectancy of African American females is about x 70.33 years, and is increasing at a rate of about .58 years/birth year 3) a. 0.2t b. three days after exposure the tumor is growing at a rate of about € 4) a. 0.42e 0.765 mm/day € 5) a. 44.928e 0.16x b. In 1987 the average player salary was increasing at a rate of about $72,607/year, while in 1997 it was increasing at a rat of $359,625/year. (Yikees!!) € 6) a. P(x) = 1,000e−.002x (x −125) € b. $175

Math 150 Logarithmic and Exponential Function

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