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 lin- ear function of time. You want to build a mathematical 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 2e if 0 te where t, is the time at which the fungus switches from exponential R(t) = { to linear growth and a is a constant. (a) For what value of a is the function R(t) continuous at t = t? (Your answer will include the unknown constant te).
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 lin- ear function of time. You want to build a mathematical 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 2e if 0 te where t, is the time at which the fungus switches from exponential R(t) = { to linear growth and a is a constant. (a) For what value of a is the function R(t) continuous at t = t? (Your answer will include the unknown constant te).
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.3: The Natural Exponential Function
Problem 33E
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Transcribed Image Text: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 lin-
ear function of time. You want to build a mathematical 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
2e if 0 <t S te
if t > te
where t, is the time at which the fungus switches from exponential
R(t) = {
to linear growth and a is a constant.
(a) For what value of a is the function R(t) continuous at t = t?
(Your answer will include the unknown constant te).
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