💬 👋 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

A population of protozoa develops with a constant relativegrowth rate of 0.7944 per member per day. On day zero thepopulation consists of two members. Find the populationsize after six days.

$$235$$

Calculus 1 / AB

Chapter 3

INVERSE FUNCTIONS

Section 4

Exponential Growth and Decay

Derivatives

Differentiation

Applications of the Derivative

Baylor University

University of Michigan - Ann Arbor

Boston College

Lectures

03:09

In mathematics, precalculu…

31:55

In mathematics, a function…

02:18

A population of protozoa d…

01:40

A certain bacteria culture…

05:41

Population Growth The rate…

01:31

A bacterial population sta…

03:53

Population Growth Suppose …

01:11

02:15

Growth of a Population The…

03:22

The number of bacteria in …

00:37

04:38

A culture of bacteria in a…

03:50

Involve exponential growth…

05:04

Suppose that the populatio…

08:21

Growth of an Insect Popula…

05:26

03:00

Under ideal conditions, a …

03:03

05:36

03:20

These exercises use the po…

04:47

01:23

The growth of a bacteria p…

Hey, guys, welcome back for this problem. We know that initially there are two protozoa. We have a growth rate of 0.7944 so I can write our exponential growth equation. Have the change and population over. The change in time is equal to que times p we can now plug in. Okay, now we're gonna want to integrate this. Who will bring the p over to the left hand side of the equation of DP overpay? No hammering the DT over to the right hand side. 0.79 for four DT. Now we can integrate both sides of the equation. When we do that, we get the natural log p minus the natural log of p o. This is a sensitive just are constant of integration. And that's what you can use for your see value for these exponential growth problems. Siegel two point 7944 t can combine our natural log terms. We've natural log P over P zero schools 0.794 for T. We can then raise each side to the swill yet p over p o t e to the 0.79 44 t which multiply each side by piece of Oh, we get P sequitur piece of Oh E 2.9 44 and we know from above that piece about is equal to So we can change this to say, P is he going toe to e 0.79 for four T and were asked to find the population at six days? So in T is equal to six, we can say P is equal toe to e 0.9, where the 2.7944 applied by six. And when you that calculation it comes out 200 34 0.99 or basically 235 so far, Answer will say population with 235 AT T seal to six. This and as a solution. Thanks for watching.

View More Answers From This Book

Find Another Textbook

Numerade Educator

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…

A population of protozoa develops with a constant relative growth of 0.7944 …

A certain bacteria culture doubles its size each day. If there are $25,000$ …

Population Growth The rate of growth $d P / d t$ of a population of bacteria…

A bacterial population starts at 500 and doubles every four days. Find a for…

Population Growth Suppose that the population of a certaincollection of …

A bacterial population starts at 200 and triples every day. Find a formula f…

Growth of a Population The rate of growth of a microbem population is given …

The number of bacteria in a culture grows at a rate that is proportional to …

The number of bacteria in a culture doubles every day. If a culture begins w…

A culture of bacteria in a Petri dish has an initial population of 1500 cell…

Involve exponential growth. Suppose a bacterial culture doubles in populatio…

Suppose that the population of a certain collection of rare Brazilian ants i…

Growth of an Insect Population The size $P$ of a certain insect population a…

Under ideal conditions, a population of rabbits has an exponential growth ra…

Involve exponential growth. Suppose a bacterial culture initially has 100 ce…

Involve exponential growth. Suppose a bacterial culture triples in populatio…

These exercises use the population growth model.Bacteria Culture It is o…

The growth of a bacteria population:$P(t)=1000 \cdot 3^{t}$If the in…

00:57

If a current $I$ passes through a resistor with resistance $R$Ohm's…

01:57

On page 431 of Physics: Calculus, 2 $\mathrm{d}$ ed. by Eugene Hecht(Pac…

02:28

Brain weight $B$ as a function of body weight $W$ in fish hasbeen modele…

09:29

(a) Show that the absolute value function $F(x)=|x|$ iscontinuous everyw…

04:09

If a ball is thrown vertically upward with a velocity of $80 \mathrm{ft} / \…

06:41

If $a$ and $b$ are positive numbers, prove that the equation

$$\frac…

01:54

Let $\ell$ be the tangent line to the parabola $y=x^{2}$ at the point $(1,1)…

02:12

$43-46=$ Find the first and second derivatives of the function.$$H(t)=\t…

01:37

Use a linear approximation (or differentials) to estimate the given number.<…

07:15

$43-44=$ (a) Prove that the equation has at least one real root(b) Use y…