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
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
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
Section2.5: Inequalities
Problem 2TU
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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.
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 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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