Experimental measurements of animal tumors indicate that the growth of cancerous tumors can be modeled by the Gompertz law: dN dt = -aN ln(bN), where N(t) is proportional to the number of cells in the tumor, and a, b > 0 are parameters. The predictions of this simple model agree surprisingly well with data on tumor growth, as long as N is not too small. 1. Use the Gompertz law to solve for N(t) with initial value N(0) = 1. 2. Compute lim N(t), and interpret what this limit means biologically. t→∞

Experimental measurements of animal tumors indicate that the growth of cancerous tumors can be modeled by the Gompertz law: dN dt = -aN ln(bN), where N(t) is proportional to the number of cells in the tumor, and a, b > 0 are parameters. The predictions of this simple model agree surprisingly well with data on tumor growth, as long as N is not too small. 1. Use the Gompertz law to solve for N(t) with initial value N(0) = 1. 2. Compute lim N(t), and interpret what this limit means biologically. t→∞

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

6th Edition

ISBN:9781337111348

Author:Bruce Crauder, Benny Evans, Alan Noell

Publisher:Bruce Crauder, Benny Evans, Alan Noell

Chapter2: Graphical And Tabular Analysis

Section2.1: Tables And Trends

Problem 1TU: If a coffee filter is dropped, its velocity after t seconds is given by v(t)=4(10.0003t) feet per...

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