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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) 0 20 1 19 20 40 7.2 2.6 50 1.5 4 10 2 18.1 16.3 5 15.5 12 (a) Predict whether a linear or exponential model will fit this data better. Justify your prediction. looking at the detta, mass decreases over time. for a linear modet, the rate of decrease would remain constant. However, the data suggests that the rate of decrease is not constant. in the intion years, the mass reduces by 1 gram per year but as time progresses, the rate of decrease becomes smalle this behaviour indicates that ar exponention model, where the rate of decay decreases over time, might be a bettter He for (b) determine the dotte linear model in the form m(t) = at+b where a and b are constants (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?

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) 0 20 1 19 20 40 7.2 2.6 50 1.5 4 10 2 18.1 16.3 5 15.5 12 (a) Predict whether a linear or exponential model will fit this data better. Justify your prediction. looking at the detta, mass decreases over time. for a linear modet, the rate of decrease would remain constant. However, the data suggests that the rate of decrease is not constant. in the intion years, the mass reduces by 1 gram per year but as time progresses, the rate of decrease becomes smalle this behaviour indicates that ar exponention model, where the rate of decay decreases over time, might be a bettter He for (b) determine the dotte linear model in the form m(t) = at+b where a and b are constants (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?

Advanced Engineering Mathematics
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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(d) Determine the equation of the exponential model in the form m(t) = axbt where a and b are constants (e) Using your equation from (d) Calculate the mass remaining after 100 years of decay (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) = axbt where a and b are constants (e) Using your equation from (d) Calculate the mass remaining after 100 years of decay (g) Using the exponential model that you determined in part (d), calculate the average annual percentage decrease in the mass of the radioactive substance.
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) 0 20 1 19 4 5 2 18.1 16.3 15.5 (a) Predict whether a linear or exponential model will fit this data better. Justify your prediction. 10 12 50 1.5 20 40 7.2 2.6 looking at the detta, mass decreases over time. for a linear model, the rate et decrease would remain constant. However, the data suggests that the rate of decrease is not constans. in the intice years, the mass reduces by 1 gram per your but as time proghesses, the rate et decrease becomes smaver this behaviour indicates that an exponention model, where the rate of decay decreases over time, might be a better fit for the data. (b) Determine the equation of the linear model in the form m(t) = at+b where a and b are constants (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?
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) 0 20 1 19 4 5 2 18.1 16.3 15.5 (a) Predict whether a linear or exponential model will fit this data better. Justify your prediction. 10 12 50 1.5 20 40 7.2 2.6 looking at the detta, mass decreases over time. for a linear model, the rate et decrease would remain constant. However, the data suggests that the rate of decrease is not constans. in the intice years, the mass reduces by 1 gram per your but as time proghesses, the rate et decrease becomes smaver this behaviour indicates that an exponention model, where the rate of decay decreases over time, might be a better fit for the data. (b) Determine the equation of the linear model in the form m(t) = at+b where a and b are constants (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?
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