Turn on thread page Beta
    • Thread Starter
    Offline

    1
    ReputationRep:
    This question is from Paper G solomon for C3 edexcel...

    (6.)
    The populations in thousands, P, of a town at time t years after 1st january 1980 is modelled by the formula

    P = 30 + 50e^0.0022t


    Use this model to estimate:

    (a) the population of the town on first january 2010,

    (b) the year in which the populaton first exceeds 84 000,


    The population in thousands, Q, of another town is modelled by the formula

    Q = 26 + 50e^0.003t


    (c) Show that th evalue of t when P = Q is a solution of the equation

    t = 1000 ln (1 + 0.08e^-0.002t)



    Anyone know how to do part (c)????
    Offline

    1
    ReputationRep:
    30 + 50e^0.002t=26 + 50e^0.003t

    4= 50e^0.003t - 50e^0.002t

    the divide everything by 50

    4/50 = e^0.003t - e^0.002t

    4/50 = e^0.002t(e^0.001t-1)

    0.08/e^0.002t = e^0.001t-1

    0.08/e^0.002t + 1 = e^0.001t

    then take ln of the lhs

    ln(0.08/e^0.002t + 1) =0.001t

    btw 0.08/e^0.002t = 0.08e^-0.002t
    therefore

    ln(0.08e^-0.002t+1)= 0.001t
    then multiply both sides by 1000

    1000ln(0.08e^-0.002t+1)=t
    hope it helped

    khalid
    • Thread Starter
    Offline

    1
    ReputationRep:
    hey thanx a lot...

    i was really stuck on that one
 
 
 
Reply
Submit reply
Turn on thread page Beta
Updated: June 11, 2006

University open days

  • University of Bradford
    All faculties Undergraduate
    Wed, 21 Nov '18
  • Buckinghamshire New University
    All Faculties Postgraduate
    Wed, 21 Nov '18
  • Heriot-Watt University
    All Schools Postgraduate
    Wed, 21 Nov '18
Poll
Black Friday: Yay or Nay?
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.