The following data pertain to cosmic ray doses measured at various altitudes. Data in image 1 Fit an exponential curve Use the result from part A to estimate the mean dose at a 3000-foot unit. Change the equation obtained in part A to the form (image 2), then use the result to rework part B. A) Fit a Gompertz curve of the shape (image 2)     ∑Xi∑Xi=16980  ∑Yi∑Yi=304  ∑Xi2∑Xi2=72743400 ∑ln(Yi)∑ln(Yi)=26.00903 ∑XiYi∑XiYi=951560  ∑Xi2Yi∑Xi2Yi=4339343800 ∑Yiln(Yi)∑Yiln(Yi)=1163.43 ∑XiYiln(Yi)∑XiYiln(Yi)=3853036   1.)  yˆ=3.340942514×e0.000155307×x   2) At X=3000, The estimated value of the mean dose at a 3000-foot unit is 5.323722.   3) yˆ=a×e−cx Y=2.096634   SOLVE A)Fit a Gompertz curve of the shape

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 22E
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The following data pertain to cosmic ray doses measured at various altitudes.
Data in image 1

  • Fit an exponential curve
  • Use the result from part A to estimate the mean dose at a 3000-foot unit.
  • Change the equation obtained in part A to the form (image 2), then use the result to rework part B.


A) Fit a Gompertz curve of the shape (image 2)

 

 

∑Xi∑Xi=16980  ∑Yi∑Yi=304  ∑Xi2∑Xi2=72743400 ∑ln(Yi)∑ln(Yi)=26.00903

∑XiYi∑XiYi=951560  ∑Xi2Yi∑Xi2Yi=4339343800 ∑Yiln(Yi)∑Yiln(Yi)=1163.43

∑XiYiln(Yi)∑XiYiln(Yi)=3853036

 

1.)  yˆ=3.340942514×e0.000155307×x

 

2) At X=3000,

The estimated value of the mean dose at a 3000-foot unit is 5.323722.

 

3) yˆ=a×e−cx

Y=2.096634

 

SOLVE

A)Fit a Gompertz curve of the shape

 

C)
ŷ = a * e-cx
D)
eeax+B
Transcribed Image Text:C) ŷ = a * e-cx D) eeax+B
Altitud
Tasa de dosis
Altitud
Tasa de dosis
y
y
50
28
4400
51
450
30
4800
58
780
32
5300
69
1200
36
Transcribed Image Text:Altitud Tasa de dosis Altitud Tasa de dosis y y 50 28 4400 51 450 30 4800 58 780 32 5300 69 1200 36
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Publisher:
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