Refer a friend and earn $50 when they subscribe to an annual planRefer Now

Get the answer to your homework problem.

Try Numerade Free for 30 Days

Like

Report

A rat has a birth mass of $8 \mathrm{g},$ and when fully grown its mass is 280 g. Using equation $(1.1 .26)$ with $a=0.25$ determine how many days it will take for the rat to reach $75 \%$ of its fully grown size.

$T\cong 139.9$ days

Calculus 2 / BC

Chapter 1

First-Order Differential Equations

Section 1

Differential Equations Everywhere

Differential Equations

Missouri State University

University of Michigan - Ann Arbor

Idaho State University

Lectures

01:11

In mathematics, integratio…

06:55

In grammar, determiners ar…

02:24

A heron has a birth mass o…

02:45

A biologist is studying th…

03:04

The activity of a sample o…

01:49

The population of a cultur…

03:45

(II) The activity of a sam…

01:46

Once an insect reaches its…

01:36

An isotope of thorium, wr…

01:23

The half-life of radium- 2…

02:33

A particular substance dec…

04:01

Solve each problem. Mu…

for the set up of this problem. We have a rodent with the birth mass off eight grams. We know that this adult will have a mass of 280 grams. We're going to use this model to find the time needed to reach 75% of the adult mass. When a is set to be equal to 0.25 to start out, let's start assigning what the variables it should be uppercase m that appears here is the adult mass. So that would be 280 grams in this problem. The next symbol is m not I m not is going to be the birth mass. So that's eight grams. In this situation, we have the variable a given to be 0.25 here and if we say t it is time to reach 75% of adult mass, that would then mean that M A T should be 0.75 times 280 so m of tea would be equal to 210 grams. This tells us our goal is to solve M of tea equals 210 14. Once we found this expression for tea will have solved this problem. So let's start out by making a substitution ample sides of this model, so we'll have 210 on the left hand side is equal to uppercase M, which is given to be 280 grams times one minus one minus. I am not, which is eight grams. Divide by uppercase M or 280 Alta power of 1/4 times the Basie exponential to the power of negative A or negative 0.25 times T divide by the quantity four times uppercase m or four times 280 to the power of 1/4 and the entire quantity, once again to the power of four. To solve this equation for tea will be using the order of operations to simplify each of these quantities. Step by step pushed out. Let's start out with this quantity. Here we can say on the next step that 210 is going to be equal to 280 times the quantity. One minus zero point 5889 times the Basie exponential And let's do on the next step, the simplification of negative 0.25 Divide by this quantity in our calculator that would turn into the quantity negative 0.1 52 nine times T Well, once again raised to the power of four. What we can do in the next step is divide both sides by this quantity to 80. So that will take to 10 divide by 2 80 We also know that from this expression here that should result in 0.75 So now we have 0.75 equals one minus 0.5889 times E to the power of negative is your a 0.15 to 90 all raised to power for on the very next step, we can take the fourth root of both sides Know the words and my calculator, or raise your 0.75 to power 1/4 raising the right hand side to power. 1/4 gives a cancellation of this outer exponents with the 1/4 next in my calculator, 0.75 to the 1/4 power or the four through to that quantity is 0.93 06 which is now set equal to one minus 0.5 89 Times e to the power negative. 0.152 nine Times t. Next, we can subtract one from both sides of this equation. If we do that. Left hand side is negative. 0.6 939 which is equal to negative zero point 5889 either the power of negative 0.15 to 9 t for next step. Let's divide both sides of this equation. By that coefficient upon that division will now obtain zero point 1178 equals e to the power negative zero point 015 to 9 t for this exponential equation. If we take the natural laudable sides, then the Basie exponential would be cancelled. So first, the natural log of zero point 1178 turns into negative 2.1384 Taking the natural log of the right hand side cancels the Basie. So we have just the exponents negative 0.15 to 9 t. Finally, we can solve this equation by dividing by the coefficient of tea. So we will obtain that T is approximately equal to 139.9 days. In other words, using the provided my bottle with that provide information, we know that this rodent will reach 75% of its adult mass in just about 240 days.

View More Answers From This Book

Find Another Textbook

Numerade Educator

In mathematics, integration is one of the two main operations in calculus, w…

In grammar, determiners are a class of words that are used in front of nouns…

A heron has a birth mass of $3 \mathrm{g},$ and when fully grown its mass is…

A biologist is studying the growth of rats on the Space Station. To determin…

The activity of a sample of $^{35}_{16}$S ($T_\frac{1}{2} =$ 87.37 days) is …

The population of a culture of bacteria is modeled by the logistic equation …

(II) The activity of a sample of $\frac{35}{16} \mathrm{S}\left(T_{\frac{1}{…

Once an insect reaches its larval stage, its massincreases linearly for …

An isotope of thorium, written as 227 Th, has a half-life of 18.4 days. How…

The half-life of radium- 224 is 3.66 days. What was the original mass of rad…

A particular substance decays in such a way that it loses half its weight ea…

Solve each problem. Muffy can eat a 25 -pound bag of dog food in28 d…

01:15

Determine the order of the differential equation.$$\left(\frac{d y}{d x}…

03:03

Determine whether the given function is an integrating factor for the given …

02:07

Determine the differential equation giving the slope of the tangent line at …

03:49

Verify that the given function is a solution to the given differential equat…

03:06

Solve the given differential equation.$y^{\prime}+\alpha y=e^{\beta x},$…

01:26

Verify that the given function (or relation) defines a solution to the given…

09:15

Determine the current in an RC circuit if the capacitor has zero charge init…

06:09

A glass of water whose temperature is $50^{\circ} \mathrm{F}$ is taken outsi…

12:02

Use Euler's method with the specified step size to determine the soluti…

92% of Numerade students report better grades.

Try Numerade Free for 30 Days. You can cancel at any time.

Annual

0.00/mo 0.00/mo

Billed annually at 0.00/yr after free trial

Monthly

0.00/mo

Billed monthly at 0.00/mo after free trial

Earn better grades with our study tools:

Textbooks

Video lessons matched directly to the problems in your textbooks.

Ask a Question

Can't find a question? Ask our 30,000+ educators for help.

Courses

Watch full-length courses, covering key principles and concepts.

AI Tutor

Receive weekly guidance from the world’s first A.I. Tutor, Ace.

30 day free trial, then pay 0.00/month

30 day free trial, then pay 0.00/year

You can cancel anytime

OR PAY WITH

Your subscription has started!

The number 2 is also the smallest & first prime number (since every other even number is divisible by two).

If you write pi (to the first two decimal places of 3.14) backwards, in big, block letters it actually reads "PIE".

Receive weekly guidance from the world's first A.I. Tutor, Ace.

Mount Everest weighs an estimated 357 trillion pounds

Snapshot a problem with the Numerade app, and we'll give you the video solution.

A cheetah can run up to 76 miles per hour, and can go from 0 to 60 miles per hour in less than three seconds.

Back in a jiffy? You'd better be fast! A "jiffy" is an actual length of time, equal to about 1/100th of a second.