### Problem StatementIf a substance decomposes at a rate proportional to the amount of the substance present, and the amount decreases from 60 ounces to 15 ounces in 2 hours, find the constant of proportionality.### Options- $ \large -\frac{1}{2} $- $ \large -\ln(2) $- $ \large -\frac{1}{4} $- $ \large \ln \left( \frac{1}{4} \right) $#### ExplanationThis question is designed to test the understanding of decay processes which follow first-order kinetics, and how to derive the constant of proportionality using given data points. In this case, the decrease in the amount of substance is used to determine the proportionality constant (decay constant) using logarithmic relationships.The proportionality follows an exponential decay model, typically represented by the equation:\[ A(t) = A_0 e^{-kt} \]where:- $ A(t) $ is the amount of substance at time $ t $,- $ A_0 $ is the initial amount of substance,- $ k $ is the decay constant,- $ t $ is the time. Given the initial and remaining amounts, along with the time elapsed, students are expected to calculate $ k $.

Answered: Image /qna-images/answer/9b2fd11a-41fc-46e5-affb-502502f9eafe.jpg

If a substance decomposes at a rate proportional to the amount of the substance present, and the amount decreases from 60 ounces to 15 ounces in 2 hours, find the constant of proportionality. O – In(2) O In()

If a substance decomposes at a rate proportional to the amount of the substance present, and the amount decreases from 60 ounces to 15 ounces in 2 hours, find the constant of proportionality. O – In(2) O In()

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

See similar textbooks

Related questions

Q: The pressure, P, (in kilopascals), volume, V, (in cm³), Related rates question: and temperature, T,…

Q: An aluminum cup of 77 cm capacity is completely filled with glycerin at 21°C. How much glycerin will…

A: Solution

Q: The rate of a certain reaction is given by the following rate law: rate - k[#][!] Jse this…

Q: A chemical was introduced into a large swimming pool to determine if it would affect the amount of…

A: NOTE: Refresh your page if you can't see any equations. . the initial amount of algae is 70 kg so…

Q: According to the Stefan-Boltzmann Law, the thermal radiation energy emitted (per unit time) by a hot…

Q: A park ranger is searching for bears in a region of the park where on average there are 12 bears per…

A: Introduction: It is given that there are 12 bears per square mile of the park. Further, the number…

Q: Substance A decomposes at a rate proportional to the amount of A present. It is found that 16 Ib of…

Q: If n birds eating continuously consume V in³ of seed in T hours, how much does in bird consume per…

A: topic- algebraic operations

Q: The mess in a restaurant can be measured by M(t). Assume that M(O) = 0, the restaurant starts out…

A: Let's consider a differential equation as follows:If M(t)=F(t), then equation 1 will be satisfied.

Q: a new substance C is to be formed by removing two units from each of two substances whose initial…

A: 1st we will formed a differential equation for amount of C and then solve it to get actual amount of…

Q: 10.) Let N represent a mass of carbon 14 (in grams), whose half-life is 5720 years. The quantity of…

Q: If a quantity grows/decays at a rate proportional to its size, its growth can be expressed as dQ/dt…

Q: Substance A decomposes at a rate proportional to the amount of A present. It is found that 18 lb of…

Q: According to the Stefan-Boltzmann Law, the thermal radiation energy emitted (per unit time) by a hot…

A: We need to find error.

Q: Find, to three decimal places, the value of x such that e−x = x.

A: Concept: The calculus helps in understanding the changes between values that are related by a…

Q: If e'z = /3 -i.Then Im (z) is %3D O a. e2 b. 0 С. 1 d. -In(2)

A: eiz=3-i Now let z=x+iy. Then, ⇒eix+iy=3-i⇒eix+i2y=3-i⇒eix-y=3-i…

Q: Substance A decomposes at a rate proportional to the amount of A present. It is found that 10 lb of…

Q: When fluid flows through a tube at a moderate velocity, the radius R of the tube is related to the…

Q: For a substance D, the time rate of conversion is proportional to the square root of the amount of x…

Q: The volume (v) of a sphere varies directly with the cube of its radius (r). If k is the constant of…

Q: A rumor spreads through a school. Let y(t) be the fraction of the population that has heard the…

A: Let y(t) be the fraction of the population that has heard the rumor at time t.The differential…

Q: Substance A decomposes at a rate proportional to the amount of A present It is found that 16 Ib of A…

Q: 14) A 300g of a certain radioactive element is left in a dish. After an hour it is found that only…

Q: Experiments indicate that glucose is absorbed by the body at a rate proportional to the amount

Q: A tank contains 200 liters of fluid in which 30 grams of salt is dissolved. Brine containing 1 gram…

Concept explainers

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.

Question

100%

### Problem Statement
If a substance decomposes at a rate proportional to the amount of the substance present, and the amount decreases from 60 ounces to 15 ounces in 2 hours, find the constant of proportionality.

### Options
- $ \large -\frac{1}{2} $
- $ \large -\ln(2) $
- $ \large -\frac{1}{4} $
- $ \large \ln \left( \frac{1}{4} \right) $

#### Explanation
This question is designed to test the understanding of decay processes which follow first-order kinetics, and how to derive the constant of proportionality using given data points. In this case, the decrease in the amount of substance is used to determine the proportionality constant (decay constant) using logarithmic relationships.

The proportionality follows an exponential decay model, typically represented by the equation:
\[ A(t) = A_0 e^{-kt} \]
where:
- $ A(t) $ is the amount of substance at time $ t $,
- $ A_0 $ is the initial amount of substance,
- $ k $ is the decay constant,
- $ t $ is the time.

Given the initial and remaining amounts, along with the time elapsed, students are expected to calculate $ k $.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Linear Equations$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

Similar questions

A toy manufacturer determined that the total cost in dollars of producing a slime kits in one day is given by C(x) = 350+2-0.012. Which of the following formulas will give an estimate of the cost of producing the 64 slime kit? %3D OC (64) O C(64)- C(63) OC (65) O (63) +C'(63) OC (63)
Sehr put $1,000 into a savings account that earns 4%/a in interest, calculated simply. How much will she have after 3 months?
Solve each question
An experiment starts with an ideal-gas sample in a sealed container with a movable piston at initial pressure of Po, initial temperature 300 K and initial volume 10 L. In the experiment, the temperature is increased to 600 K, while the piston is moved until the volume decreases to 4 L. What will the final pressure be equal to? 2Po 2/3 Po O 1/2 Po 5Po O Po 52