(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
Chapter6: Exponential And Logarithmic Functions
Section6.8: Fitting Exponential Models To Data
Problem 3TI: Table 6 shows the population, in thousands, of harbor seals in the Wadden Sea over the years 1997 to...
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Question
Do part e
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
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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