Turn on thread page Beta
    • Thread Starter
    Offline

    9
    ReputationRep:
    The mass of a substance is decreasing exponentially. Its mass now is 150 grams and its mass, m grams, at a time t years from now is given by m = 150e^–kt, where k is a positive constant. Find, in terms of k, the number of years from now at which the mass will be decreasing at a rate of 3 grams per year.

    dm/dt = -150ke^-kt
    3/-150k = e^-kt
    ln(2/-150k) = lne^-kt
    ln(2/-150k) = -kt
    ln(2/-150k) / -k = t

    the mark scheme says that the answer is :
    -1/k ln(1/50k)
    or
    1/k ln(50k)
    or
    ln50 + lnk/k

    how do i end up with any of the above and where have i gone wrong in my working out??
    • Community Assistant
    Offline

    18
    ReputationRep:
    Community Assistant
    (Original post by elvss567)
    The mass of a substance is decreasing exponentially. Its mass now is 150 grams and its mass, m grams, at a time t years from now is given by m = 150e^–kt, where k is a positive constant. Find, in terms of k, the number of years from now at which the mass will be decreasing at a rate of 3 grams per year.

    dm/dt = -150ke^-kt
    3/-150k = e^-kt
    ln(2/-150k) = lne^-kt
    ln(2/-150k) = -kt
    ln(2/-150k) / -k = t

    the mark scheme says that the answer is :
    -1/k ln(1/50k)
    or
    1/k ln(50k)
    or
    ln50 + lnk/k

    how do i end up with any of the above and where have i gone wrong in my working out??
    The mass is decreasing so  \frac{dm}{dt} is negative.
    • Thread Starter
    Offline

    9
    ReputationRep:
    (Original post by NotNotBatman)
    The mass is decreasing so  \frac{dm}{dt} is negative.
    so -3 instead of 3? is the rest of the working out allright?
    • Community Assistant
    Offline

    18
    ReputationRep:
    Community Assistant
    (Original post by elvss567)
    so -3 instead of 3? is the rest of the working out allright?
    Yes and yes.
    • Thread Starter
    Offline

    9
    ReputationRep:
    (Original post by NotNotBatman)
    Yes and yes.
    thankyou
 
 
 
Reply
Submit reply
Turn on thread page Beta
Updated: November 7, 2017

University open days

  • University of Exeter
    Undergraduate Open Days - Exeter Campus Undergraduate
    Wed, 24 Oct '18
  • University of Bradford
    Faculty of Health Studies Postgraduate
    Wed, 24 Oct '18
  • Northumbria University
    All faculties Undergraduate
    Wed, 24 Oct '18
Poll
Do protests make a difference in political decisions?
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

Equations

Best calculators for A level Maths

Tips on which model to get

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.