Suppose that the population of a country in the year 2000 was 19.0 million and grew to 22.6 million in 2010 . Write a model of the form p t − p 0 e " , where p t is the population in millions, t years after the year 2000 . Round the growth rate to 5 decimal places.
Suppose that the population of a country in the year 2000 was 19.0 million and grew to 22.6 million in 2010 . Write a model of the form p t − p 0 e " , where p t is the population in millions, t years after the year 2000 . Round the growth rate to 5 decimal places.
Solution Summary: The author calculates a model of the form P(t)=P_0ekt.
Suppose that the population of a country in the year
2000
was
19.0
million and grew to
22.6
million in
2010
. Write a model of the form
p
t
−
p
0
e
"
,
where
p
t
is the population in millions,
t
years after the year
2000
. Round the growth rate to
5
decimal places.
1. Show that the vector field
F(x, y, z)
=
(2x sin ye³)ix² cos yj + (3xe³ +5)k
satisfies the necessary conditions for a conservative vector field, and find a potential function for
F.
1. Newton's Law of Gravitation (an example of an inverse square law) states that the magnitude
of the gravitational force between two objects with masses m and M is
|F|
mMG
|r|2
where r is the distance between the objects, and G is the gravitational constant. Assume that the
object with mass M is located at the origin in R³. Then, the gravitational force field acting on
the object at the point r = (x, y, z) is given by
F(x, y, z) =
mMG
r3
r.
mMG
mMG
Show that the scalar vector field f(x, y, z) =
=
is a potential function for
r
√√x² + y² .
Fi.e. show that F = Vf.
Remark: f is the negative of the physical potential energy, because F = -V(-ƒ).
2. Suppose f(x) = 3x² - 5x. Show all your work for the problems below.
Using and Understanding Mathematics: A Quantitative Reasoning Approach (6th Edition)
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Area Between The Curve Problem No 1 - Applications Of Definite Integration - Diploma Maths II; Author: Ekeeda;https://www.youtube.com/watch?v=q3ZU0GnGaxA;License: Standard YouTube License, CC-BY