A bacterial culture is growing according to the model y = 1.50 / ( 1 + 0.2 e − 0.5 t ) , t ≥ 0 , where y is the culture weight (in grams) and t is the time (in hours). Find the weight of the culture after 0 hours, 1 hour, and 10 hours. What is the limit of the model as t increases without bound?
A bacterial culture is growing according to the model y = 1.50 / ( 1 + 0.2 e − 0.5 t ) , t ≥ 0 , where y is the culture weight (in grams) and t is the time (in hours). Find the weight of the culture after 0 hours, 1 hour, and 10 hours. What is the limit of the model as t increases without bound?
Solution Summary: The author calculates the weight of a bacterial culture after 0hours and the limit of the model as t increases without any bound.
A bacterial culture is growing according to the model
y
=
1.50
/
(
1
+
0.2
e
−
0.5
t
)
,
t
≥
0
, where y is the culture weight (in grams) and t is the time (in hours). Find the weight of the culture after 0 hours, 1 hour, and 10 hours. What is the limit of the model as t increases without bound?
Find the Laplace transform of f(t). f(t) = 8t6 + 3t4 - 2t + 5
42.37590 is correct and 42.11205 is incorect.
3. (i) Using the definition of the line integral of a vector field, calculate the
line integral
L³
F.dy
of the vector field F: R² → R² given by
F(x, y) = (y, x),
and where the curve & is the unit semi-circle centred at the origin, located in
the upper half-plane and oriented in the anticlockwise direction.
Hint. Represent the curve y as the join of two curves y = 71 + 1/2 (see Example 8.9
in the Notes).
[20 Marks]
(ii) Calculate the same integral using Green's Theorem.
[10 Marks]
Chapter 4 Solutions
Calculus: An Applied Approach (Providence College: MTH 109)
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.
01 - What Is A Differential Equation in Calculus? Learn to Solve Ordinary Differential Equations.; Author: Math and Science;https://www.youtube.com/watch?v=K80YEHQpx9g;License: Standard YouTube License, CC-BY
Higher Order Differential Equation with constant coefficient (GATE) (Part 1) l GATE 2018; Author: GATE Lectures by Dishank;https://www.youtube.com/watch?v=ODxP7BbqAjA;License: Standard YouTube License, CC-BY