Find the solution of each of the following problems. Identify the given, required, and the formula to be used. Used the formula given below. 5. Bacteria in a certain culture increase at a rate proportional to the number present. If the original number increases by 50% in hour, in how many hours can one expect three times the original number and five times the original number? Exponential Growth and Decay • If y is a differentiable function of t, such that y > 0 and dy/dt = ky for some constant k, then: A = Pert y = Cekt P(t) = Pekt • P is called the initial value of P(t) and k is called the constant of proportionality. You get a growth equation when k> 0 and a decay equation when k < 0.
Find the solution of each of the following problems. Identify the given, required, and the formula to be used. Used the formula given below. 5. Bacteria in a certain culture increase at a rate proportional to the number present. If the original number increases by 50% in hour, in how many hours can one expect three times the original number and five times the original number? Exponential Growth and Decay • If y is a differentiable function of t, such that y > 0 and dy/dt = ky for some constant k, then: A = Pert y = Cekt P(t) = Pekt • P is called the initial value of P(t) and k is called the constant of proportionality. You get a growth equation when k> 0 and a decay equation when k < 0.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Find the solution of each of the following problems. Identify the given, required, and the formula to be used.
Used the formula given below
5. Bacteria in a certain culture increase at a rate proportional to the number present. If the original number
1
hour, in how many hours can one expect three times the original number and five times
2
increases by 50% in
the original number?
Exponential Growth and Decay
• If y is a differentiable function of t, such that y
>0 and dy/dt = ky for some constant k, then:
A = Pert
y = Cekt
P(t) = Pekt
• P, is called the initial value of P(t) and k is called the
constant of proportionality. You get a growth equation
when k> 0 and a decay equation when k < 0.
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