Answered: 50. Fungal Growth As a fungus grows,…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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As a fungus grows, its rate of growth changes. Young fungi grow exponentially, while in larger fungi growth slows, and the total dimensions of the fungus increase as a linear function of time. You want to build a mathematcal model that describes the two phases of growth. Specifically if R(t) is the rate of growth given as a function of time, t, then you model.

50. Fungal Growth As a fungus grows, its rate of growth changes. Young
fungi grow exponentially, while in larger fungi growth slows, and the total
dimensions of the fungus increase as a linear function of time. You want to
build a mathematical model that describes the two phases of growth.
Specifically if R(f) is the rate of growth given as a function of time, t, then
you model
2e
if 0t < tc
la
if t > tc
R(t)
where te is the time at which the fungus switches from exponential to
linear growth and a is a constant
a. For what value of a is the function R(t) continuous at t te? (Your
answer will include the unknown constant te)
b. Assume that te = 2. Draw the graph of R(t) as a function of t

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