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(e) Using your equation from (d) Calculate the mass remaining after 100 years of decay malgo) 20.06(0.950) 9.12 100 miled

(e) Using your equation from (d) Calculate the mass remaining after 100 years of decay malgo) 20.06(0.950) 9.12 100 miled

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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A radioactive substance with original mass of 20 grams decays (or reduces in mass) according to the data in the table below Time, t (years) Mass, m (grams) (a) Predict whether a linear or exponential model will fit this data better. Justify your prediction. 0 20 1 19 m(t) => m(t) = 4 2 18.1 16.3 =at+b 5 15.5 10 12 0-3707€ 117.9042 20 7.2 looking at the detta, mass decreases over time. for a linear modet, the rate of decrease would reman constant. Howeve the data suggests that the rate of decrease is not constant. in the intice years the mass reduces by 1 gram per year but as time preghesses, the rate et decrease becomes sma this behaviour indicates that ar exponention model, where He rate of decay decreases over time, might be a bettla fit for the dater. (b) Determine the equation of the linear model in the form m(t) = at+b where a and b are constants 40 2.6 50 1.5 (c) Find the residuals plot on your calculator for the linear model and reflect on your prediction in part (a). Was it accurate? Why or why not? Yes
Transcribed Image Text:A radioactive substance with original mass of 20 grams decays (or reduces in mass) according to the data in the table below Time, t (years) Mass, m (grams) (a) Predict whether a linear or exponential model will fit this data better. Justify your prediction. 0 20 1 19 m(t) => m(t) = 4 2 18.1 16.3 =at+b 5 15.5 10 12 0-3707€ 117.9042 20 7.2 looking at the detta, mass decreases over time. for a linear modet, the rate of decrease would reman constant. Howeve the data suggests that the rate of decrease is not constant. in the intice years the mass reduces by 1 gram per year but as time preghesses, the rate et decrease becomes sma this behaviour indicates that ar exponention model, where He rate of decay decreases over time, might be a bettla fit for the dater. (b) Determine the equation of the linear model in the form m(t) = at+b where a and b are constants 40 2.6 50 1.5 (c) Find the residuals plot on your calculator for the linear model and reflect on your prediction in part (a). Was it accurate? Why or why not? Yes
(d) Determine the equation of the exponential model in the form m(t) = axb' where a and b are constants (e) Using your equation from (d) Calculate the mass remaining after 100 years of decay muco mit taxb t => mit =20.80610.951 € 20.06(0.95e) 9.12 miled (g) Using the exponential model that you determined in part (d), calculate the average annual percentage decrease in the mass of the radioactive substance.
Transcribed Image Text:(d) Determine the equation of the exponential model in the form m(t) = axb' where a and b are constants (e) Using your equation from (d) Calculate the mass remaining after 100 years of decay muco mit taxb t => mit =20.80610.951 € 20.06(0.95e) 9.12 miled (g) Using the exponential model that you determined in part (d), calculate the average annual percentage decrease in the mass of the radioactive substance.
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