53-56 - Finding Logarithmic Functions Find the function of the form y = log, x whose graph is given. 53. У 54. уд (5, 1) 1 5 x (3. -1) 55. 56. У4 (9, 2) (3. 4) 1 1 3 6 9 x 3.
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53–56 ■ Finding Logarithmic Functions Find the function of
the form y loga x whose graph is given.
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- 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?An initial amount of a radioactive substance y0 is given, along with information about the amount remaining after a given time t in appropriate units. For an equation of the form y = y0 ekt that models the situation, give the exact value of k in terms of natural logarithms.9. y0 = 60 g; After 3 hr, 20 g remain.The function y = log2x is transformed into the graph of y = log(x + 2) - 3. a) Describe (in a correct order) the transformations that must be applied to the graph of y = log2x to get the graph of y = log2(x + 2) - 3 B) sketch the graph of y = loga(x + 2) - 3 C) State the domain, range, equation of the vertical asymptote, the coordinates of the x-intercept and the coordinates of the y-intercept. If the graph does not have an x or y-intercept, be sure to explicitly state that as the case.
- Using properties of logarithmic to condense the logarithm of Log y + 8 log zA virus is spreding by contact and if you get infected you become a carrier for an unlimited time. In a isolated population with P people, the rate of infection at the time t (months after 1. January 2020) is proportional with the product og (1) the amount y(t) of poeple who are infected (meaning the amount that are contagious) and (2) the amount of people who are not infected (meaning the amount that can get infected). This means the spreding of the virus follows logistic growth. 1/10 of the population is infected 1. January 2020. If 1/5 og the population is infected after one month, how many are infected after one year?A certain quantity has an initial value of 8.2 and grows at a rate of 8.5% per year. Give an exponential function that describes this quantity after x years. a) f(x) = 8.2(1.085)^xb) f(x) = 7.2(1.853)^xc) f(x) = 6.2(1.083)^xd) f(x) = 5.2(1.085)^x
- Scientists can determine the age of ancient objects by themethod of radiocarbon dating. The bombardment of theupper atmosphere by cosmic rays converts nitrogen to aradioactive isotope of carbon, C, with a half-life of about5730 years. Vegetation absorbs carbon dioxide through theatmosphere and animal life assimilates C through foodchains. When a plant or animal dies, it stops replacing itscarbon and the amount of C begins to decrease throughradioactive decay. Therefore the level of radioactivity mustalso decay exponentially.A parchment fragment was discovered that had about74% as much C radioactivity as does plant material onthe earth today. Estimate the age of the parchment.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.A virus infects by contact and if you are first infected you stay a carrier for unlimited time. In an isolated population with P inhabitants the the rate of infections by time (in moths after 1/1 2020) is proportional with the product of 1 the amount infected, meaning people that are infectious, 2 the amount not infected, meaning people that can be infected, which means the functions follows logistic growth. A tenth of the population is infected 1/1 2020. If a fifth of the population is infected one month later, how many are infected one year later?
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