# Starting Log and Ln Chapter 4 (Need Help)

• Apr 18th 2006, 04:58 PM
OverclockerR520
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?
• Apr 18th 2006, 08:51 PM
CaptainBlack
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
• Apr 19th 2006, 02:24 AM
OverclockerR520
I typed them back in as best I could.
• Apr 19th 2006, 04:30 AM
CaptainBlack
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:

$\displaystyle M=L\ \frac{r}{12}\ \frac{(1+r/12)^{12k}}{(1+r/12)^{12k}-1}$

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

$\displaystyle M=90000\ \frac{0.07}{12}\ \frac{(1+0.07/12)^{360}}{(1+0.07/12)^{360}-1}\approx \$598.77
$b) Total interest$\displaystyle TI$is total repaid minus the principal:$\displaystyle
TI=360*598.77-90000=\$125557$

c)Putting $\displaystyle r=0.08$ and $\displaystyle k=25$ into the formula give that for $\displaystyle L=90000$, $\displaystyle M=\$694.64$, 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$\displaystyle \$800$ then the loan is:

$\displaystyle L=\frac{800}{694.64}\ 90000 \approx \$103650$RonL (you will need to check the arithmetic - no guarantee given) • Apr 19th 2006, 06:08 AM OverclockerR520 Thank you for your help! Im checking it in the calc right now :D • Apr 19th 2006, 10:26 AM CaptainBlack 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:$\displaystyle
y=79.041+6.39x-e^{3.261-0.993x}
$for$\displaystyle 1/4 \le x \le 6$For a two year old$\displaystyle x=2$so the typical height is:$\displaystyle
y=79.041+6.39\times 2-e^{3.261-0.993\times 2}=91.821-e^{1.275}
$Now your calculator should have an "exp" function. This allows you to find$\displaystyle e^{1.275}=\exp(1.275)\approx 3.579$, so:$\displaystyle
y=95.400 \mbox{cm}
\$

RonL