Turn on thread page Beta
    • Thread Starter
    Offline

    0
    ReputationRep:
    Thanks for all the help!
    Offline

    4
    ReputationRep:
    You can say dx/dt = -64 - kx

    Separate the variables and integrate both sides. You know when t = 0, x = 2 so you can include that information with your constant.

    Hint: Might be easier if you put your constant of integration in the form "ln a" so it comes out nicely when you rearrange after integrating.
    • Thread Starter
    Offline

    0
    ReputationRep:
    (Original post by Ben121)
    You can say dx/dt = -64 - kx

    Separate the variables and integrate both sides. You know when t = 0, x = 2 so you can include that information with your constant.

    Hint: Might be easier if you put your constant of integration in the form "ln a" so it comes out nicely when you rearrange after integrating.
    I don't have a clue how to get that equation.
    Offline

    10
    ReputationRep:
    Initially, 2kg of actinium is present and the rate of decay of its mass is 64g/year"...so x=2 and dx/dt = -0.064 (Kg/year) when t=0.

    " Subsequently, t years later when the actinium has a mass xkg, the rate of decrease of mass is proportional to the value of x."
    This means that dx/dt = -kx where k is a positive constant.

    So, -0.064 = -k*2 (when t=0), hence k=0.032.
    Therefore dx/dt = -0.032x.

    Key is to understand the key words: rate = derivative, rate of decay=negative derivative.
    proportional to x mean "constant multiplied by x"
    • Thread Starter
    Offline

    0
    ReputationRep:
    (Original post by vc94)
    Initially, 2kg of actinium is present and the rate of decay of its mass is 64g/year"...so x=2 and dx/dt = -0.064 (Kg/year) when t=0.

    " Subsequently, t years later when the actinium has a mass xkg, the rate of decrease of mass is proportional to the value of x."
    This means that dx/dt = -kx where k is a positive constant.

    So, -0.064 = -k*2 (when t=0), hence k=0.032.
    Therefore dx/dt = -0.032x.

    Key is to understand the key words: rate = derivative, rate of decay=negative derivative.
    proportional to x mean "constant multiplied by x"
    Hi there,

    thanks for the help. Sorry but you explain how -k^2 = -0.064 please?
    Offline

    10
    ReputationRep:
    We're told that: x=2 and dx/dt = -0.064 (Kg/year) when t=0.

    And since dx/dt = -kx, then substituting we get -0.064 = -k*2 (* means multilply)
 
 
 
Reply
Submit reply
Turn on thread page Beta
Updated: April 6, 2011
The home of Results and Clearing

1,316

people online now

1,567,000

students helped last year

University open days

  1. London Metropolitan University
    Undergraduate Open Day Undergraduate
    Sat, 18 Aug '18
  2. Edge Hill University
    All Faculties Undergraduate
    Sat, 18 Aug '18
  3. Bournemouth University
    Clearing Open Day Undergraduate
    Sat, 18 Aug '18
Poll
A-level students - how do you feel about your results?
Useful resources

Make your revision easier

Maths

Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

Equations

How to use LaTex

Writing equations the easy way

Student revising

Study habits of A* students

Top tips from students who have already aced their exams

Study Planner

Create your own Study Planner

Never miss a deadline again

Polling station sign

Thinking about a maths degree?

Chat with other maths applicants

Can you help? Study help unanswered threads

Groups associated with this forum:

View associated groups

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

Write a reply...
Reply
Hide
Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.