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Radioactive substances A and B have decay constants of 0.02 and 0.05, respectively. If a mixture of these two substances at time t=0 contains MA grams of A and MB grams of B, then a model for the total amount y of the mixture present at time t is y=MAе-0.02t + Mge-0.05t. Suppose the initial amounts MA and M are unknown, but a scientist is е able to measure the total amount present at several times and records the following points (t₁, y₁): (10, 21.33), (11, 20.69), (12, 20.09), (14, 18.88), and (15, 18.34). a. Describe a linear model that can be used to estimate MA and MB. b. Find the least-squares curve based on the equation y=MAе -0.02t + Mge-0.05t

Radioactive substances A and B have decay constants of 0.02 and 0.05, respectively. If a mixture of these two substances at time t=0 contains MA grams of A and MB grams of B, then a model for the total amount y of the mixture present at time t is y=MAе-0.02t + Mge-0.05t. Suppose the initial amounts MA and M are unknown, but a scientist is е able to measure the total amount present at several times and records the following points (t₁, y₁): (10, 21.33), (11, 20.69), (12, 20.09), (14, 18.88), and (15, 18.34). a. Describe a linear model that can be used to estimate MA and MB. b. Find the least-squares curve based on the equation y=MAе -0.02t + Mge-0.05t

MATLAB: An Introduction with Applications
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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Radioactive substances A and B have decay constants of 0.02 and 0.05, respectively. If a mixture of these two substances at time t = 0 contains MA grams of A and MB grams of B, then a model for the total amount y of the mixture -0.02t ,-0.05t = MAе + MBe present at time t is y= Suppose the initial amounts MA and MB are unknown, but a scientist is able to measure the total amount present at several times and records the following points (t₁, Y₁): (10, 21.33), (11, 20.69), (12, 20.09), (14, 18.88), and (15, 18.34). a. Describe a linear model that can be used to estimate MÅ and MB. -0.02t b. Find the least-squares curve based on the equation y = Me A -0.05t + Mge
Transcribed Image Text:Radioactive substances A and B have decay constants of 0.02 and 0.05, respectively. If a mixture of these two substances at time t = 0 contains MA grams of A and MB grams of B, then a model for the total amount y of the mixture -0.02t ,-0.05t = MAе + MBe present at time t is y= Suppose the initial amounts MA and MB are unknown, but a scientist is able to measure the total amount present at several times and records the following points (t₁, Y₁): (10, 21.33), (11, 20.69), (12, 20.09), (14, 18.88), and (15, 18.34). a. Describe a linear model that can be used to estimate MÅ and MB. -0.02t b. Find the least-squares curve based on the equation y = Me A -0.05t + Mge
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