Population growth. Some underdeveloped nations have population doubling times of 50 years. At what continuous compound rate is the population growing? (Use the population growth model in Problem 47.) 47. World population. A mathematical model for world population growth over short intervals is given by P = P 0 e r t where P 0 = population at time t = 0 r = continuous compound rate of growth t = time in years P = population at time t How long will it take the world population to double if it continues to grow at its current continuous compound rate of 1.13% per year?
Population growth. Some underdeveloped nations have population doubling times of 50 years. At what continuous compound rate is the population growing? (Use the population growth model in Problem 47.) 47. World population. A mathematical model for world population growth over short intervals is given by P = P 0 e r t where P 0 = population at time t = 0 r = continuous compound rate of growth t = time in years P = population at time t How long will it take the world population to double if it continues to grow at its current continuous compound rate of 1.13% per year?
Solution Summary: The author explains the rate r at which the population is growing. The world population growth over short intervals is given by P=P_0ert.
Population growth. Some underdeveloped nations have population doubling times of 50 years. At what continuous compound rate is the population growing? (Use the population growth model in Problem 47.)
47. World population. A mathematical model for world population growth over short intervals is given by
P
=
P
0
e
r
t
where
P
0
=
population
at
time
t
=
0
r
=
continuous
compound
rate
of
growth
t
=
time
in
years
P
=
population
at
time
t
How long will it take the world population to double if it continues to grow at its current continuous compound rate of 1.13% per year?
4.
Prove: If x {0, 1} then x² -
-x=0.
5.
6.
Prove by contrapositive: Suppose x is a real number. If x>0 then x + 16 0.
Prove by contradiction: Suppose n is an integer. Then n² - n+10.
Hint: You might try organizing the proof by cases on whether n is even or odd. Is n² - n+1 even or odd?
Let f(x)=7x²-2x and g(x) = 5x+3. Find f[g(k)].
Use the method of reduction of order to find a second solution to
ty"-(4t+4)+(4t+8)y = 0, t> 0
Given y₁(t) = e²t
Y2(t) =
Give your answer in simplest form (ie no coefficients)
Chapter 3 Solutions
Calculus for Business, Economics, Life Sciences, and Social Sciences (14th Edition)
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject 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