Question: Suppose that substance A is converted into substance B at a rate that, at any time t, is proportional to the square of the amount

Suppose that substance A is converted into substance B at a rate that, at any time t, is proportional to the square of the amount of A. This situation occurs, for instance, when it is necessary for two molecules of A to collide to create one molecule of B. Set up the differential equation that is satisfied by y = f (t), the amount of substance A at time t. Sketch a solution.

Step by Step Solution

★★★★★

3.53 Rating (160 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

y ky k ... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Applied Calculus Questions!

When a certain liquid substance A is heated in a flask, it decomposes into a substance B at such a rate (measured in units of A per hour) that at any time t is proportional to the square of the...

a differential equation is given along with the field or problem area in which it arises. Classify each as an ordinary differential equation (ODE) or a partial differential equation (PDE), give the...

Suppose that a ball is dropped from the upper observation deck of the CN Tower in Toronto, 450 m above the ground. Find the velocity of the ball after 2 seconds. Through experiments carried out four...

1. Show that "the rate of change of y is proportional to y" supports the model y = Cekx. 2. If BY = 4 , k is a constant, and if y = 3 when x = 1, and y = 8 when x = e, find y when x = 2. 3. The rate...

Business Research Methodology- Question Bank 1 1. When the marketing department of an organization attempts to determine the amount of time the managers in this department spend at their computers in...

Business Research MethodologyQuestion Bank 1 1. When the marketing department of an organization attempts to determine the amount of time the managers in this department spend at their computers in...

10. An experimenter has some degree of control over the: a. independent variable. b. correlative variable. c. history effect. d. All of the above, if the experiment is conducted properly. 11. If a...

In Chapter 3, you were introduced to 3 types of costs associated with a manufactured product ? direct materials, direct labor, and manufacturing overhead. Explain how these costs are associated with...

the benefit of international trade are derived from Chapter 1: Introduction 1) The benefits of international trade are derived from A) differences in climate and geography B) labor productivity C)...

The wedding date for a couple is quickly approaching, and the wedding planner must provide the caterer an estimate of how many people will attend the reception so that the appropriate quantity of...

Dilberts Department Store is trying to determine how many Hanson T-shirts to order. Currently the shirts are sold for $21, but at later dates the shirts will be offered at a 10% discount, then a 20%...

7. 1. Why should management be concerned about paying its invoices on a timely basis? 2. Why is it important for a firm to maintain a satisfactory credit rating? 3. Suppose you are the new controller...

Human Development Index, part 4. In Exercise 63 we examined the relationship between log(GDPPC) and HDI for 172 countries. The number of cell phone subscribers (per 1000 people) is also positively...

Find confidence intervals for each pair of differences in population means. Comment on how this shows where differences can be established and where it is plausible there are no differences between...

Can you conclude that you have found strong evidence of a cause-and-effect relationship between the three groups that received different kinds of feedback and their aggressiveness toward their...

To what broader population are you willing to generalize your findings? Explain. The following table provides descriptive statistics on the measurements for aggression: Experimental group Control...

EBIT: The Generic Publications Textbook Company sells all of its books for $100 per book, and it currently costs $50 in variable costs to produce each text. The fixed costs, which include...

You have been assigned to examine the financial statements of Bridgewater, Inc. for the year ended December 31, 2018. You discover the following situations in February 2019. Bridgewater, Inc. has not...

Roth Incorporated experienced the following transactions for Year 1, its first year of operations: Issued common stock for $80,000 cash. Purchased $245,000 of merchandise on account. Sold merchandise...