Problem

Shown is the graph of traffic on an Internet serv…

01:24

Question

Answered step-by-step

Problem 71 Hard Difficulty

A bacteria population is 4000 at time $ t = 0 $ and its rate of growth is $ 1000 \cdot 2^t $ bacteria per hour after $ t $ hours. What is the population after one hour?

Video Answer

Solved by verified expert

Textbook Answer

Official textbook answer

Video by Leon Druch

Numerade Educator

This textbook answer is only visible when subscribed! Please subscribe to view the answer

Watch More Solved Questions in Chapter 5

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

Problem 10

Problem 11

Problem 12

Problem 13

Problem 14

Problem 15

Problem 16

Problem 17

Problem 18

Problem 19

Problem 20

Problem 21

Problem 22

Problem 23

Problem 24

Problem 25

Problem 26

Problem 27

Problem 28

Problem 29

Problem 30

Problem 31

Problem 32

Problem 33

Problem 34

Problem 35

Problem 36

Problem 37

Problem 38

Problem 39

Problem 40

Problem 41

Problem 42

Problem 43

Problem 44

Problem 45

Problem 46

Problem 47

Problem 48

Problem 49

Problem 50

Problem 51

Problem 52

Problem 53

Problem 54

Problem 55

Problem 56

Problem 57

Problem 58

Problem 59

Problem 60

Problem 61

Problem 62

Problem 63

Problem 64

Problem 65

Problem 66

Problem 67

Problem 68

Problem 69

Problem 70

Problem 71

Problem 72

Problem 73

Problem 74

Video Transcript

Okay here in this problem we're looking at population growth uh T. Represents hours. So when T equals zero the population is 4000. T. Equals zero. Means in the very beginning. Before we even started counting time uh T. Equals one. Would mean one hour has passed. T equals zero means we're at the very beginning no time has passed. So if the population is 4008 equals zero that means we were starting with a population of 4000. Now the rate of growth is given by this expression 1000 times two to the T. Power where T. Is the number of hours. And we want to find a population uh the entire population after one hour. Well after one hour uh We are going to have a population that we started with. But also we're going to have uh more population more bacteria. Because we're going to experience some growth. Because after the end of one hour where T. Is going to be one we're going to have some growth in uh number of bacteria. So the population after one hour Is going to be the original 4000 that we started with the original population plus uh the growth in the population. The growth in the population that takes place during the first hour is going to be given by this expression. So 4000 the original population plus uh the increase in the population as it grew during that first hour. So we have to do 1000 times two. And since we're looking for the population after one hour that means T. Is going to be one. Only one hour has elapsed. So to to the T. Will be two to the first. So this will be the entire population. 4000 is the population we started with 1000 times two to the first power. Is the growth in the population during the first hour. Now to to the first power is just too times 1000 will give you 2000 Plus. The original 4000 is a total of 6000. So what is the total population at the end of one hour? 6000 4000 That we started with plus 2 2000 that the bacteria grew by during that first hour. So we start with 4000 Uh bacteria. And then during the first hour they grew 2000 more bacteria. For a total of 6000 bacteria.

Get More Help with this Textbook

James Stewart

Calculus: Early Transcendentals

View More Answers From This Book

Find Another Textbook

Study Groups

Study with other students and unlock Numerade solutions for free.

Problem

Shown is the graph of traffic on an Internet serv…

This textbook answer is only visible when subscribed! Please subscribe to view the answer

More Answers

Related Courses

Calculus: Early Transcendentals

Related Topics

Discussion

Top Calculus 1 / AB Educators

Caleb Elmore

Kristen Karbon

Samuel Hannah

Michael Jacobsen

Calculus 1 / AB Courses

Recommended Videos

Watch More Solved Questions in Chapter 5

Video Transcript

James Stewart

Calculus: Early Transcendentals

Grace He

Anna Marie Vagnozzi

Heather Zimmers

Kristen Karbon

This textbook answer is only visible when subscribed! Please subscribe to view the answer

Calculus: Early Transcendentals

Caleb Elmore

Kristen Karbon

Samuel Hannah

Michael Jacobsen

James StewartCalculus: Early Transcendentals

Grace He

Anna Marie Vagnozzi

Heather Zimmers

Kristen Karbon

James Stewart

Calculus: Early Transcendentals