(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 (g) Using the exponential model that you determined in part (d), calculate the average annual percentage decrease in the mass of the radioactive substance.
(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 (g) Using the exponential model that you determined in part (d), calculate the average annual percentage decrease in the mass of the radioactive substance.
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.7: Applications
Problem 14EQ
Related questions
Question
This is a follow up question please answer d,e and g
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)
0
Mass, m (grams) 20
4
5
16.3 15.5
(a) Predict whether a linear or exponential model will fit this data better. Justify your prediction.
m(t)
1
19
=1
2
18.1
looking at the dotta, mass decreases over time. for a linear
modet, the rate et decrease would remain constant. However,
the data suggests that the rate of decrease is not constant.
in the intial years the mass reduces by 1 gram per year
but as time
the rate et decrease
becomes smaner
=at+b
mit)
this behaviour indi ba that ar exponention model, where
He rate of decay decreases over time, might be a bettter
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
10
12
50
1.5
40
20
7.2 2.6
-6-3707€ 117.9042
(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:(d) Determine the equation of the exponential model in the form m(t) = axb¹ 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.
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