9. The half-life of a radioactive element can be modelled by M =G)where M, is the initialmass of the element and M is the mass that remains after a certain amount of time. The half-life of theelement isa. 3 hoursb. 2 hoursc. 6 hoursd. t hourse. 0.5 hours

If y=f(x), then the independent variable x is called the input of the function, and the dependent…

Answered: 9. The half-life of a radioactive…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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3. A wildlife manager counted 1800 mice in a 10-km² area of forest. It is predicted that the mouse population in this area will grow exponentially according to the function P(t) = 1800e 0.03/ where P(t) is the > years. mouse population and t is the time, in a) How long will it take for the mouse population to i) double ii) triple b) Find the rate of change of the mouse population after i) 10 years ii) 25 years c) At what rate is the mouse population growing at the time when its number has tripled?
The table shows the age-adjusted death rates per 100,000 citizens for heart disease in a certain country. Complete parts (a) and (b) below. (a) Find an exponential model of the form f(t)=yob' for these data, where t=0 corresponds to the year 2000.Use the first and last data points to find a function. 1(t)=¹ (Round to two decimal places as needed.) (b) Assuming the model remains accurate, estimate the death rate in 2019 and 2024. The death rate in 2019 will be (Round to one decimal place as needed.) people per 100,000 The death rate in 2024 will be (Round to one decimal place as needed.) people per 100,000. Year 2000 2002 2004 2006 2008 2010 2012 2014 Death Rate 257.4 239.4 215.0 211.9 185.6 178.9 171.8 166.0
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Consider two cities with size given by an exponential model. City A has size Ao (1.25)'and City B has size Bo(0.95) Ag and B. are their respective initial sizes. In 1925, Ao = 12000 and Bo = 11500. Will the two towns ever have the same size as time passes by? (Enter YES or NO) Type your answer and submit
The exponential growth model of a population in a certain city is A= 20e0.05t, where A is the size of the population in thousands in a particular year, and t is the number of years from the year 2000. a) What is the population of the city in the year 2000? b) What is the population of the city in the year 2020? C) If the rate of change increased after 2020 to 10%, in what year that the population be 200,000? d) What could be the initial population if the number of people is 10, 0000, 000 in 12 years with the same growth rate?
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Radium-226 decays exponentially so that if Q0 represents the initial amount present, the quantity Q remaining after t years is given by Q=Q0(0.99572)^t. (a) How long will it take until only half the original quantity Q0remains? round your answer to two decimal places. (i.e. find the half-life of radium-226) (b) Find the constant kk, accurate to three decimal places, such that Q=Q0e^kt

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9. The half-life of a radioactive element can be modelled by M = Mo (-)" where Mo is the initial mass of the element and M is the mass that remains after a certain amount of time. The half-life of the element is