# Math Help - Linear Interpolation

1. ## Linear Interpolation

Hi all,

For an interview I'm going next week I have to do a maths test, now I haven't done maths since school so I'm a little out of touch! I was quite good at maths in my time but have forgotten a lot of the principles. I was wondering if I could get some help with the following questions - I'd really appreciate it...

1. You can get a loan for $1000 over the next 35 days at an interest rate of 4.25%. You can also get a loan of$1000 over the next 56 days for 4.79%. Use linear interpolation to calculate the total amount in $s in interest you might expect to pay on a loan of$1000 over the next 47 days.

2. Provide reasoning that the equation

$
10 = exp(-2x) + 2^x
$

has at least one solution in the range 0<x<5

Use the Newton Raphson technique to find an approximate solution to the equation.

3. This is a random question but its bothering me a lot!!
A group of students scored an averafe of 65% in an exam. The standard deviation of these results was 1%. A second group of students scored an average of 60% with a standard deviation of 2%. What is the mean and standard deviation of the two groups of students as a whole if 20 students were in each group?

I'd really appreciate any help - the maths part of my brain is a little rusty at the moment!

2. This section is based on known information, the DAYS
56 - 35 = 21
47 - 35 = 12
12 / 21 = 0.571428571

This section models the previous secion, but has a piece missing, the one interest rate.
4.79 - 4.25 = 0.54
X.xxx - 4.25 = yyyy
yyyy / 0.54 = 0.571428571

Can you solve for yyyy?

Of course, you must also realize that yyyy is only the interest RATE. The question asks for .