7-10 - Evaluating Exponential Functions Use a calculator to evaluate the function at the indicated values. Round your answers to three decimals. 9. g(x) = (})**': g(}). g(V2). g(-3.5). g(-1,4)
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- Tuberculosis (TB) is one of the top 10 causes of death worldwide. According to the World Health Organization (WHO), deaths from TB have fallen by an average of 1.2% per year between 2000 and 2015. In the year 2000, there were approximately 2.5 million deaths from TB. Part 1. Use the given data to create an exponential decay function to model the number of deaths from TB in terms of years, tt, where t=0 represents the year 2000. Part 2. Use this function to determine the year in which the number of deaths from TB was 2.1 million.Some biorlogos model thenumberof S species in afixed area A (e.g. an island) with therelationto thespecies- log(S) = log(c) + k log(A ) where c and k are positive constants that depend on the type of species and the hábitat. a) Of the equationorclearance S. (b) Using the subsection(a),if k = 4 and the area is tripled, whyis thatmagnitude increased by the number of species?At the beginning of a study, a certain culture of bacteria has a population of 40. The population grows according to a continuous exponential growth model. After 5 days, there are 124 bacteria. a)Let t be the time (in days) since the beginning of the study, and let y be the number of bacteria at time t. Write a formula relating y to t. Use exact expressions to fill in the missing parts of the formula. Do not use approximations. b)How many bacteria are there 7 days after the beginning of the study? Do not round any intermediate computations, and round your answer to the nearest whole number.
- Suppose an exponential curve passes through the point (0,3) with a growth factor of 2. Write the equation for the exponential function y=LIMIT OF EXPONENTIAL FUNCTION 3x+5x5x-_3x 4x-1 1+x21-y2 log2x+3x-2 Imagine that you are a local government leader in your municipality. How can you use exponential functions as basis for making significant decisions in line with your role? You may choose one aspect or issue in your municipality to ilustrate your answer. In which aspect or situation in your academic life can you relate the concept of the limit of logarithmic fuctions? How does this topic influence your positive outlook in life?The mass of a substance, which follows a continuous exponential growth model, is being studied in a lab. The doubling time for this substance was observed to be 4 hours. There were 87.1mg of the substance present at the beginning of the study. (a)Let t be the time (in hours) since the beginning of the study, and let y be the amount of the substance at time t . Write a formula relating y to t .Use exact expressions to fill in the missing parts of the formula.Do not use approximations. =yet (b)How much will be present in 11 hours? Do not round any intermediate computations, and round your answer to the nearest tenth. mg
- The mass of a substance, which follows a continuous exponential growth model, is being studied in a lab. The doubling time for this substance was observed to be 4 hours. There were 87.1 mg of the substance present at the beginning of the study.(a)Let t be the time (in hours) since the beginning of the study, and let y be the amount of the substance at time t.Write a formula relating y to t.Use exact expressions to fill in the missing parts of the formula.Do not use approximations. (b)How much will be present in 11 hours?Do not round any intermediate computations, and round your answer to the nearest tenth.A report tells us that in 2019 there were 800 of a certain type of animal in an area, but that the population decreased by 4% that year. For purposes of this problem we assume that this 4% annual rate of decrease continues. Find an exponential model that gives the animal population ? as a function of ? in years since 2019.The initial size of a population is 1000, and it has the given instantaneous growth or decay rate per year. −85% (a) Find an exponential model f(x) = Cerx for the population, where x is measured in years.f(x) =
- On June 25, 2020, North Carolina reported 1009 new CoVID-19 cases.On July 14th, 2020, North Carolina reported 1956 new cases. If weassume that the growth is exponential, find the function that modelsthe number of new cases as a function of t, the number of days sinceJune 25. (Note, July 14th is t=19.) If this growth continues, how manynew cases would there be in 60 days?Identify 10 applications of exponential functions in different fields of specialization. Complete the table that includes the sources and description of the application.Energy consumption On the first day of the year (t = 0), a city uses electricity at a rate of 2000 MW. That rate is projected to increase at a rate of 1.3% per year.a. Based on these figures, find an exponential growth function for the power (rate of electricity use) for the city.b. Find the total energy (in MW-yr) used by the city over four full years beginning at t = 0.c. Find a function that gives the total energy used (in MW-yr) between t = 0 and any future time t > 0.
