Hey there! Sign in to join this conversationNew here? Join for free
    • Thread Starter
    Offline

    0
    ReputationRep:
    Hi all
    A researcher discoversthat between 2008 and 2010, the number of messages sent on Twitter (called tweets) increased exponentially. She investigates the number of tweets from apopular author, and finds that they can be modelledby the equation u = 20×(1.8)t, where u is the total number of tweets sent, and t is the number of months since the author became a Twitter user, where 0t 8.1. Use the method shown in Unit 13, Subsection 5.2 to find the month in which the exponential model predicts that the total number of tweets sent will first reach 500
    i did it like this u = log(10) * 25 log(10) * 1.8 = 45 but 45 doesnt seem right if you put 45 in the model u= 20*(1.8)*45 = 1620 which is far more than 500. but if i put 14 in the model u = 20- *(1.8) * 14 = 504 tweets somonth 14 seems more right put the logs dont make sense .Any help with logs please.Eggie
    • Community Assistant
    • Welcome Squad
    Offline

    20
    ReputationRep:
    Community Assistant
    Welcome Squad
    (Original post by eggie)
    Hi all
    A researcher discoversthat between 2008 and 2010, the number of messages sent on Twitter (called tweets) increased exponentially. She investigates the number of tweets from apopular author, and finds that they can be modelledby the equation u = 20×(1.8)t, where u is the total number of tweets sent, and t is the number of months since the author became a Twitter user, where 0t 8.1. Use the method shown in Unit 13, Subsection 5.2 to find the month in which the exponential model predicts that the total number of tweets sent will first reach 500
    i did it like this u = log(10) * 25 log(10) * 1.8 = 45 but 45 doesnt seem right if you put 45 in the model u= 20*(1.8)*45 = 1620 which is far more than 500. but if i put 14 in the model u = 20- *(1.8) * 14 = 504 tweets somonth 14 seems more right put the logs dont make sense .Any help with logs please.Eggie
    Do you mean u=20 \cdot 1.8^t?

    So then u=500 and 500=20 \cdot 1.8^t

    Take logs of both sides and use some log rules:
    log(500)=log(20 \cdot 1.8^t)=log(20)+log(1.8^t)

    Im not sure where you are pulling log(10) from.
    • Thread Starter
    Offline

    0
    ReputationRep:
    (Original post by RDKGames)
    Do you mean u=20 \cdot 1.8^t?

    So then u=500 and 500=20 \cdot 1.8^t

    Take logs of both sides and use some log rules:
    log(500)=log(20 \cdot 1.8^t)=log(20)+log(1.8^t)

    Im not sure where you are pulling log(10) from.
    Hi RDk
    It gives base log(10) in the examples so thats what im using to answer the question. It asks for month 1 , month 2 month 3 and month 8 which are
    month 1 = u = 20 * 1.8 * 1 = 36
    month 2 = u = 20* 1.8 * 2 = 72
    month 3 = u = 20* 1.8 * 3 = 108
    month 8 = u = 20 * 1.8 * 8 = 288

    so the models scale factor is 100% so month 7 = u = 20* 1.8 * 7 = 252 so month 14 =504 tweets as i said in the example.

    u = 20*(1.8)^t which month tweets reach 500
    I am dividing 20 by 500 to get 25 and putting 25 in the logs but taking the log20 and log1.8^t still cant get 14 tried different scenarios but still stuck .

    any extra help appreciated
    • Community Assistant
    • Welcome Squad
    Offline

    20
    ReputationRep:
    Community Assistant
    Welcome Squad
    (Original post by eggie)
    Hi RDk
    It gives base log(10) in the examples so thats what im using to answer the question. It asks for month 1 , month 2 month 3 and month 8 which are
    month 1 = u = 20 * 1.8 * 1 = 36
    month 2 = u = 20* 1.8 * 2 = 72
    month 3 = u = 20* 1.8 * 3 = 108
    month 8 = u = 20 * 1.8 * 8 = 288

    so the models scale factor is 100% so month 7 = u = 20* 1.8 * 7 = 252 so month 14 =504 tweets as i said in the example.

    u = 20*(1.8)^t which month tweets reach 500

    t is bounded between 0 and 8.1. It CANNOT be 14 months. The equation is u=20\cdot 1.8^t and NOT u=20\cdot 1.8t otherwise it will never reach 500 within 8 months.

    Also, what do you mean by:
    I am dividing 20 by 500 to get 25 and putting 25 in the logs but taking the log20 and log1.8^t still cant get 14 tried different scenarios but still stuck .
    First of all, 20 divided by 500 is NOT 25. Secondly, that's the wrong order of operation. Lastly, putting 25 in the logs doesn't make sense, I think you meant taking the log of 500.

    You are looking for the time when u=500. So plug it into your equation and solve for t.

    500=20 \cdot 1.8^t
    \rightarrow 25=1.8^t and now solve it using logs.
    • Thread Starter
    Offline

    0
    ReputationRep:
    (Original post by RDKGames)
    t is bounded between 0 and 8.1. It CANNOT be 14 months. The equation is u=20\cdot 1.8^t and NOT u=20\cdot 1.8t otherwise it will never reach 500 within 8 months.

    Also, what do you mean by:


    First of all, 20 divided by 500 is NOT 25. Secondly, that's the wrong order of operation. Lastly, putting 25 in the logs doesn't make sense, I think you meant taking the log of 500.

    You are looking for the time when u=500. So plug it into your equation and solve for t.

    500=20 \cdot 1.8^t
    \rightarrow 25=1.8^t and now solve it using logs.
    Hi RDK

    I charted a graph using the equation and got month 5.47 when tweets reach 500

    i did it this way using log base 10 and get the same answer

    u = log(10)*25 / log(10) * 1.8 = 5.47 graph gives the same answer when i plot
    the point 500. Now only one thing i cant work out is tweets for month 8 but i think it is 2204. Is that right can u check my answers fot tweets

    month 1 = 36
    month2 = 64.8 or 65
    month3 = 116.6 or 117
    month8 = 2204

    are these right please

    thanks

    Eggie
    • Community Assistant
    • Welcome Squad
    Offline

    20
    ReputationRep:
    Community Assistant
    Welcome Squad
    (Original post by eggie)
    Hi RDK

    I charted a graph using the equation and got month 5.47 when tweets reach 500

    i did it this way using log base 10 and get the same answer

    u = log(10)*25 / log(10) * 1.8 = 5.47 graph gives the same answer when i plot
    the point 500. Now only one thing i cant work out is tweets for month 8 but i think it is 2204. Is that right can u check my answers fot tweets

    month 1 = 36
    month2 = 64.8 or 65
    month3 = 116.6 or 117
    month8 = 2204

    are these right please

    thanks

    Eggie
    Yes those are correct.
    • Thread Starter
    Offline

    0
    ReputationRep:
    (Original post by RDKGames)
    Yes those are correct.
    Hi RDk

    Thanks for the help only last thing left and finish my End of module assessment
    and finish the course is the scale factor how do i work out the scale factor of the
    expontenial model and percentage increase in total number tweets sent

    thanks
    Eggie

    found the scale factor which 1.80 or 80% but how do i find the percentage increase in total number of tweets sent
    from 36 tweets to 2204 tweets so how do i find the percentage increase please.
    Offline

    3
    ReputationRep:
    (Original post by eggie)
    Hi RDk

    Thanks for the help only last thing left and finish my End of module assessment
    and finish the course is the scale factor how do i work out the scale factor of the
    expontenial model and percentage increase in total number tweets sent

    thanks
    Eggie

    found the scale factor which 1.80 or 80% but how do i find the percentage increase in total number of tweets sent
    from 36 tweets to 2204 tweets so how do i find the percentage increase please.
    (2204-36)/36 * 100% = 6022%.
 
 
 
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • Poll
    Brussels sprouts
    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
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • 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

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