Answered: The following data pertain to cosmic…

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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Question

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

Altitud
Tasa de dosis
Altitud
Tasa de dosis
y
y
50
28
4400
51
450
30
4800
58
780
32
5300
69
1200
36

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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