Results 1 to 6 of 6

Math Help - Starting Log and Ln Chapter 4 (Need Help)

  1. #1
    Newbie
    Joined
    Mar 2006
    Posts
    10

    Starting Log and Ln Chapter 4 (Need Help)

    Hello,

    In class I am breifing chapter 4 through 4.5 then we are jumping to 9 so I have to get 4 down quickly. In my homework are two questions I'm getting fustrated on. The first should be simple since its basically substituiting for variables. The second delts with the relationship between ln and to the power variable "e". Any help would be much appreciated as I have typed out the questions in full below, thanks!

    Question on Chapter 4
    use formula below

    M=Lrk/12(k-1) where k=(1+r/12) to the power of 12t
    and t is the number of years that loan is in effect

    Some lending institutions calculate the monthly payment M on a loan of L dollars at an interest rate r (expressed as a decimal) by using the formula





    a) Find the monthly payment on a 30–year $90,000 mortgage if the interest rate is 7%


    b) Find the total interest paid on the loan in (a).


    c) Find the largest 25–year home mortgage that can be obtained at an interest rate of 8% if the monthly payment is to be $800.



    Question on LOG and LN
    The Jenss model is generally regarded as the most accurate formula for predicting the height of preschool children. If y is the height in cm and x is the age in years, then


    y=79.041 + 6.39x-e to the power of 3.261-0.993x
    for 1/4 (less than or eual to) x (less than or equal to 6) years.


    What is the height of a typical two year old?
    Last edited by OverclockerR520; April 19th 2006 at 02:23 AM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by OverclockerR520
    Hello,

    In class I am breifing chapter 4 through 4.5 then we are jumping to 9 so I have to get 4 down quickly. In my homework are two questions I'm getting fustrated on. The first should be simple since its basically substituiting for variables. The second delts with the relationship between ln and to the power variable "e". Any help would be much appreciated as I have typed out the questions in full below, thanks!

    Question on Chapter 4
    Some lending institutions calculate the monthly payment M on a loan of L dollars at an interest rate r (expressed as a decimal) by using the formula


    where and t is the number of years the loan is in effect


    a) Find the monthly payment on a 30–year $90,000 mortgage if the interest rate is 7%


    b) Find the total interest paid on the loan in (a).


    c) Find the largest 25–year home mortgage that can be obtained at an interest rate of 8% if the monthly payment is to be $800.



    Question on LOG and LN
    The Jenss model is generally regarded as the most accurate formula for predicting the height of preschool children. If y is the height in cm and x is the age in years, then


    for years.


    What is the height of a typical two year old?
    Vital equations have disappeared from you post.

    RonL
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Mar 2006
    Posts
    10
    I typed them back in as best I could.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by OverclockerR520
    Question on Chapter 4
    use formula below

    M=Lrk/12(k-1) where k=(1+r/12) to the power of 12t
    and t is the number of years that loan is in effect

    Some lending institutions calculate the monthly payment M on a loan of L dollars at an interest rate r (expressed as a decimal) by using the formula





    a) Find the monthly payment on a 30–year $90,000 mortgage if the interest rate is 7%


    b) Find the total interest paid on the loan in (a).


    c) Find the largest 25–year home mortgage that can be obtained at an interest rate of 8% if the monthly payment is to be $800.

    First lets write your repayment formula clearly:

    <br />
M=L\ \frac{r}{12}\  \frac{(1+r/12)^{12k}}{(1+r/12)^{12k}-1}<br />

    Now 7% is a rate of 0.07, so plugging the given values for part a) into
    the formula gives:

    <br />
M=90000\ \frac{0.07}{12}\  \frac{(1+0.07/12)^{360}}{(1+0.07/12)^{360}-1}\approx \$598.77<br />

    b) Total interest TI is total repaid minus the principal:

    <br />
TI=360*598.77-90000=\$125557<br />

    c)Putting r=0.08 and k=25 into the formula give that for L=90000, M=\$694.64,
    but the monthly repayments over a fixed period at a fixed rate
    is proportional to the loan amount. so if the repayments are to be \$800 then the loan is:

    L=\frac{800}{694.64}\ 90000 \approx \$103650

    RonL

    (you will need to check the arithmetic - no guarantee given)
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Mar 2006
    Posts
    10
    Thank you for your help!

    Im checking it in the calc right now
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by OverclockerR520
    Question on LOG and LN
    The Jenss model is generally regarded as the most accurate formula for predicting the height of preschool children. If y is the height in cm and x is the age in years, then


    y=79.041 + 6.39x-e to the power of 3.261-0.993x
    for 1/4 (less than or eual to) x (less than or equal to 6) years.


    What is the height of a typical two year old?
    Lets write the equation clearly:

    <br />
y=79.041+6.39x-e^{3.261-0.993x}<br />

    for 1/4 \le x \le 6

    For a two year old x=2 so the typical height is:

    <br />
y=79.041+6.39\times 2-e^{3.261-0.993\times 2}=91.821-e^{1.275}<br />

    Now your calculator should have an "exp" function. This allows you to find
    e^{1.275}=\exp(1.275)\approx 3.579, so:

    <br />
y=95.400 \mbox{cm}<br />

    RonL
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. new chapter start
    Posted in the Trigonometry Forum
    Replies: 2
    Last Post: January 18th 2010, 11:48 AM
  2. Problem (differentiation chapter)
    Posted in the Math Topics Forum
    Replies: 1
    Last Post: April 17th 2009, 11:24 AM
  3. Linear chapter question
    Posted in the Math Topics Forum
    Replies: 2
    Last Post: February 7th 2009, 03:57 AM
  4. Chapter One Calculus Question
    Posted in the Calculus Forum
    Replies: 5
    Last Post: August 30th 2008, 03:22 PM
  5. Calc 1 chapter 1 - Easy for you
    Posted in the Calculus Forum
    Replies: 1
    Last Post: August 28th 2008, 01:35 PM

Search Tags


/mathhelpforum @mathhelpforum