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- In this exercise, we consider data from the Statistical Abstract of the United States on the fraction of women married for the first time in 1960 whose marriage reached a given anniversary number. The data show that the fraction of women who reached their fifth anniversary was 0.928. After that, for each one-year increase in the anniversary number, the fraction reaching that number drops by about 2%. These data describe constant percentage change, so it is reasonable to model the fraction M as an exponential function of the number n of anniversaries since the fifth. (a) What is the yearly decay factor for the exponential model?(b) Find an exponential model for M as a function of n. (Let n = 0 represent the fifth anniversary.) M = (c) According to your model, what fraction of women married for the first time in 1960 celebrated their 50th anniversary? (Take n = 45.) Round your answer to three decimal places.In this exercise, we consider data from the Statistical Abstract of the United States on the fraction of women married for the first time in 1960 whose marriage reached a given anniversary number. The data show that the fraction of women who reached their fifth anniversary was 0.928. After that, for each one-year increase in the anniversary number, the fraction reaching that number drops by about 2%. These data describe constant percentage change, so it is reasonable to model the fraction M as an exponential function of the number n of anniversaries since the fifth.What exponential function will pass through both (0,6) and (1,3)?
- When a breeding group of animals is introduced into a restricted area such as a wildlife reserve, the population can be expected to grow rapidly at first but to level out when the population grows to near the maximum that the environment can support. Such growth is known as logistic population growth, and ecologists sometimes use a formula to describe it. The number N of deer present at time t (measured in years since the herd was introduced) on a certain wildlife reserve has been determined by ecologists to be given by the function below. (Round your answers down to the nearest whole number.) N = 12.35 0.01 + 0.54t (a) How many deer were initially on the reserve? deer(b) Calculate N(12).N(12) = deer (c) Express the number of deer present after 17 years using functional notation. N Calculate the number of deer present after 17 years. deer(d) How much increase in the deer population do you expect from the 12th to the 17th year? deerWhen a breeding group of animals is introduced into a restricted area such as a wildlife reserve, the population can be expected to grow rapidly at first but to level out when the population grows to near the maximum that the environment can support. Such growth is known as logistic population growth, and ecologists sometimes use a formula to describe it. The number N of deer present at time t (measured in years since the herd was introduced) on a certain wildlife reserve has been determined by ecologists to be given by the function below. (Round your answers down to the nearest whole number.) N = 12.33 0.01 + 0.54t (a) How many deer were initially on the reserve? deer(b) Calculate N(12).N(12) = deer(c) Express the number of deer present after 17 years using functional notation. N Calculate the number of deer present after 17 years. deer(d) How much increase in the deer population do you expect from the 12th to the 17th year? deerAccording to worldometer.info, the world population in 2020 is 7, 794, 798, 739 and the population growth rate is 1.05%. (4.1) Using the Malthusian model, project the world population in 2025. (4.2) Using the logistic growth model, with K = 10, 000, 000, 000 and k = 1.05%, project the world population in 2025.
- A patient takes a 300 mg tablet for the control ofhigh blood pressure every morning at the same time. The concentrationof the drug in the patient’s system decays exponentially ata constant hourly rate of k = 0.12. After the patient has taken the medication for at least six months, what quantity of drug is in the patient’s body just before the next regularly scheduled morning tablet is taken?a certain strain of bacteria is placed in a petri dish as a part of an experiment. The number of bacteria present in the petri dish, b(t), grows exponentially as a function of t, where t is measured in minutes since the start of the experiment. However, the lab assistant carelessly forgot to measure the number of bacteria at the start of the experiment. If there are 600 bacteria present after 1 minute and 900 bacteria present after 3 minutes, model the number of bacteria b(t) as an exponential function of tImagine that COVID-19 had spread exponentially in Maine since the first case (on March 12). Using the model f(t)=A02t/d with A0=1 and t= number of days since March 12, find D with the knowledge that there were 7,603 total cases on Nov. 7, 240 days after March 12.
- Which function produces an exponential graph through (0, 1) and (1, e)?A colony of bacteria is grown under ideal conditions in a laboratory so that the population increases exponentially with time. After 9 minutes there are 1,000 bacteria and after 15 minutes there are 3,000. How many are there after 33 minutes? Do NOT approximate any values.A certain quantity Q has an intitial value of 13 and decays by 4% each year. Give an exponential function that describes this quantity
