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In Section 1.4 we modeled the world population from 1900 to 2010 with the exponential function$$P(t)=(1436.53) \cdot(1.01395)^{t}$$where $t=0$ corresponds to the year 1900 and $P(t)$ is measured in millions. According to this model, what was the rate of increase of world population in $1920 ?$ In $1950 ?$ In $2000 ?$

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00:45

Frank Lin

01:23

Heather Zimmers

Calculus 1 / AB

Chapter 3

Differentiation Rules

Section 4

The Chain Rule

Derivatives

Differentiation

Campbell University

Oregon State University

University of Michigan - Ann Arbor

Boston College

Lectures

04:40

In mathematics, a derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a moving object with respect to time is the object's velocity. The concept of a derivative developed as a way to measure the steepness of a curve; the concept was ultimately generalized and now "derivative" is often used to refer to the relationship between two variables, independent and dependent, and to various related notions, such as the differential.

44:57

In mathematics, a differentiation rule is a rule for computing the derivative of a function in one variable. Many differentiation rules can be expressed as a product rule.

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In Section 1.4 we modeled …

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In this example we modeled…

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World population growth In…

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In this section we modeled…

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06:39

With $t$ in years since $1…

01:05

The population, $P(t),$ of…

04:50

The world population in bi…

01:35

According to the World Ban…

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In Section 10.4, Exercise …

02:58

uh huh. In this problem we are given the population team and millions of the function of two years, 20 0, 1900 has given us P. T equals 14 36 or 1436.58 and 1.1395 inches the parrot to We want to find the rate of change of p in 1920 19 52,000. As a note given here where the Astros indicates, we're going to use differentiation with the chain rule to find the derivative or rate of change of the population of 13 to 15. So different changes in the chain will gives us P prime T. That is the rate of change DPD teen as d b u d s b u L n d d D X. Because this is an exponential function. Thus we have G p t equals 14 36.53 times. Bu bu 1.1395 T. And l n b f l n 1.1395 times the u d x already Dutt, which is 51. Thus, we have DPT in 1920 19 52,000. By funding in t v equals 20 5100 as the numbers given here.

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