💬 👋 We’re always here. Join our Discord to connect with other students 24/7, any time, night or day.Join Here!

Get the answer to your homework problem.

Try Numerade Free for 7 Days

Like

Report

The table gives the population of the world $ P(t), $ in millions, where $ t $ is measured in years and $ t = 0 $ corresponds to the year 1900.(a) Estimate the rate of population growth in 1920 and in 1980 by averaging the slopes of two secant lines.(b) Use a graphing device to find a cubic function (a third- degree polynomial) that models the data.(c) Use your model in part (b) to find a model for the rate of population growth.(d) Use part (c) to estimate the rates of growth in 1920 and 1980. Compare with your estimates in part (a).(e) In Section 1.1 we modeled $ P(t) $ with the exponential function$ f(t) = (1.43653 \times 10^9) \cdot (1.01395)^t $Use this model to find a model for the rate of population growth.(f) Use your model in part (e) to estimate the rate of growth in 1920 and 1980. Compare with your estimates in parts (a) and (d).(g) Estimate the rate of growth in 1985.

a) 78.5 million/yearb) $a \approx-0.0002849003, b \approx 0.52243312243$, $c \approx-6.395641396,$ and $d \approx 1720.586081$c) $P^{\prime}(t)=3 a t^{2}+2 b t+c($ in millions of people per year)d) 14.16 mil/yr in 1920, 71.72 mil/yr in 1980, both values are smaller than the estimates from part (a)e) $f^{\prime}(t)=p q^{t} \ln q$f) $f^{\prime}(20) \approx 26.25$ million/year, $f^{\prime}(80) \approx 60.28$ million/yearg) $P^{\prime}(85) \approx 76.24$ million/year and $f^{\prime}(85) \approx 64.61$ million/year

08:02

Heather Z.

Calculus 1 / AB

Chapter 3

Differentiation Rules

Section 7

Rates of Change in the Natural and Social Sciences

Derivatives

Differentiation

Missouri State University

Harvey Mudd College

University of Michigan - Ann Arbor

University of Nottingham

Lectures

03:09

In mathematics, precalculu…

31:55

In mathematics, a function…

16:06

The table gives estimates …

12:25

02:23

World population growth In…

07:54

01:08

In Section 1.4 we modeled …

02:46

The relative growth rate o…

01:17

Modeling Data The table sh…

01:35

World Population The relat…

03:13

Models of population growt…

06:49

The table gives the US pop…

So for the given problem, we're going to be looking at rates of change, especially in this case, we want to be estimating the rate of population growth in 1920 in 1980 by averaging the slopes of the two second lines. So in this case looking at the change in time, there's 60 year change. Um and then subtracting the population over that 60 year time period, we see there's going to be a growth of 78.5 million per year. And then we want to use the graphing device to model the data so that's going to be are a value. So this is going to be a X. Cubed plus three X squared plus C. X plus D. And we get that A is negative 0.2849 B. Is 0.52 to four. Uh See is a negative 6.39564 And then d will be 17 20 plus 0.586 So that right there gives us we'll find this using possibly Excel or some other computing tool that we can model the data.

In mathematics, precalculus is the study of functions (as opposed to calculu…

In mathematics, a function (or map) f from a set X to a set Y is a rule whic…

The table gives estimates of the world population, in millions, from 1750 to…

The table gives estimates of the world population, inmillions, from 1750…

World population growth In Example 1.4 .3 we modeled the world population fr…

In Section 1.4 we modeled the world population from 1900 to 2010 with the ex…

The relative growth rate of world population has been decreasing steadily in…

Modeling Data The table shows the populations $y$ (in millions) of the Unite…

World Population The relative growth rate of world population has been decre…

Models of population growth have the general form $d N / d t=f(N),$ where $f…

The table gives the US population from 1790 to 1860.(a) Use a graphing c…