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From population growth and continuously compounded interest to radioactive decay and Newton’s law of cooling, exponential functions are ubiquitous in nature. In this section, we examine exponential growth and decay in the context of some of these applications.
- 4.2 Linear Approximations and Differentials
Analysis. Using a calculator, the value of 9.1 9.1 to four...
- 5.6 Integrals Involving Exponential and Logarithmic Functions
As mentioned at the beginning of this section, exponential...
- 3.9 Derivatives of Exponential and Logarithmic Functions
Assume the population is increasing at a rate of 5% per...
- 6.2 Determining Volumes by Slicing
The formulas for the volume of a sphere (V = 4 3 π r 3), (V...
- 6.4 Arc Length of a Curve and Surface Area
Arc Length of the Curve x = g(y). We have just seen how to...
- Introduction
Textbook content produced by OpenStax is licensed under a...
- Key Terms
This free textbook is an OpenStax resource written to...
- Key Equations
This free textbook is an OpenStax resource written to...
- 4.2 Linear Approximations and Differentials
29 wrz 2023 · The equation dP dt = P(0.025 − 0.002P) is an example of the logistic equation, and is the second model for population growth that we will consider. We expect that it will be more realistic, because the per capita growth rate is a decreasing function of the population.
Calculate the average rate of change for population. Using the population at t = 0 (1980) and t = 20 (2000), apply the formula P (20) − P (0) 20 − 0. Population in 1980: 181,843 Population in 2000: 197,800 Average rate of change = \frac {197,800 - 181,843} {20} 05.
17 sie 2024 · The logistic differential equation can be solved for any positive growth rate, initial population, and carrying capacity.
Recall that one model for population growth states that a population grows at a rate proportional to its size. We begin with the differential equation \[\dfrac{dP}{dt} = \dfrac{1}{2} P. \label{1}\] Sketch a slope field below as well as a few typical solutions on the axes provided.
In this section we look at some applications of the derivative by focusing on the interpretation of the derivative as the rate of change of a function. These applications include acceleration and velocity in physics, population growth rates in biology, and marginal functions in economics.
INTRODUCTION TO CALCULUS. MATH 1A. Unit 31: Calculus and Economics. Lecture. 31.1. Calculus is important in economics. This is an opportunity to review extrema problems and get acquainted with jargon in economics.
