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. if 0ststc 2e R(t) = a if t> te where t is the time at which the fungus switches from exponential to linear growth and a is a constant. Complete parts a and b below. (a) For what value of a is the function R(t) continuous at t=t,? If a =, then R(t) is continuous at t=t. (Type an expression using t, as the variable. Type an exact answer in terms of e.)
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. if 0ststc 2e R(t) = a if t> te where t is the time at which the fungus switches from exponential to linear growth and a is a constant. Complete parts a and b below. (a) For what value of a is the function R(t) continuous at t=t,? If a =, then R(t) is continuous at t=t. (Type an expression using t, as the variable. Type an exact answer in terms of e.)
Chapter4: Linear Functions
Section4.2: Modeling With Linear Functions
Problem 45SE: In 2004, a school population was 1,001. By 2008the population had grown to 1,697. Assume...
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Transcribed Image Text: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.
if 0ststc
2e
R(t) =
a
if t>te
where t is the time at which the fungus switches from exponential to linear growth and a is a constant. Complete parts a and b below.
(a) For what value of a is the function R(t) continuous at t =t,?
If a =
then R(t) is continuous at t= t.
(Type an expression using t, as the variable. Type an exact answer in terms of e.)
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