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In the biological and physical sciences, a common model
Chapter 11, Problem 65E(choose chapter or problem)
Problem 65E
In the biological and physical sciences, a common model for proportional growth over time is
E ( Y ) = 1 − e−βt ,
where Y denotes a proportion and t denotes time. Y might represent the proportion of eggs that hatch, the proportion of an organism filled with diseased cells, the proportion of patients reacting to a drug, or the proportion of a liquid that has passed through a porous medium. With n observations of the form (yi , ti ), outline how you would estimate and then form a confidence interval for β.
Questions & Answers
QUESTION:
Problem 65E
In the biological and physical sciences, a common model for proportional growth over time is
E ( Y ) = 1 − e−βt ,
where Y denotes a proportion and t denotes time. Y might represent the proportion of eggs that hatch, the proportion of an organism filled with diseased cells, the proportion of patients reacting to a drug, or the proportion of a liquid that has passed through a porous medium. With n observations of the form (yi , ti ), outline how you would estimate and then form a confidence interval for β.
ANSWER:
Step 1 of 6
In this exercise we have the following model:
According to this we have:
because
To estimate the parameter 
where
According to this, in this exercise we have:
where 
