1029
- Run Multiple Choice Generator at
h:\shares\physics
- Run Core Problems by giving the program 163 as your
'course'--enter this when asked for your 3-digit course number.
- Do choice #3, then do choice #9.
- If you miss a problem be sure to click on Comment and
explain what you do and do not understand about the question and the given
solution
Problem Number 7
If a(n) = a(n-1) + 9, with a(0) = -9, then what is the
value of a( 310)?
Compounding $1000 initial principle continuously, for 1 year,
at 100% annual interest:
- If we compound just once we end up with $2000, which is
obvious.
- If we compound twice then we get to add 50%, then add
another 50% to the resulting amount. Adding 50% is the same as multiply
by 1.5 So we multiply the initial principle by 1.5, then multiply the
result by 1.5. We end up with $1000 * 1.5 * 1.5 = $1000 * 1.5^2 = $2250.
- If we compound, say, 100 times we get to add 1%, then add
another 1% to the resulting amount, etc., 100 times. Adding 1% is the
same as multiply by 1.01 So we multiply the initial principle by 1.01,
then multiply the result by 1.01, etc., 100 times. We end up with $1000
* 1.01^100 = $2704, a factor of 2.704.
- If we compound n times then we get to add 100% / n, a total
of n times.
- Adding 100% / n = 1.00 / n or just 1/n is the same as
multiplying by 1 + 1 / n. So we multiply the initial principle by 1+1/n,
then multiply the result by 1+1/n, etc., n times.
- We end up with $1000 * (1 + 1/n) ^ n.
- As n -> infinity compounding approaches continuous and (1 +
1/n) ^ n approaches e. e is approximately 2.71828.
If we compound interest annually at annual rate 8% then if
we start with $1000, how much do we have after 5 years?
Compounding annually we multiply our principle by 1.08 every
year, so we end up with $1000 * 1.08^5 = $1469.32.
If we compound interest monthly at annual rate 8% then if
we start with $1000, how much do we have after 5 years?
Compounding monthly we multiply our principle by 1 + .08 / 12
= 1.006667 every month. In 5 years we do this 5 * 12 times, so we end up
with $1000 * 1.006667^(5 * 12) = $1487.90.
If we compound interest continuously at annual rate 8% then
if we start with $1000, how much do we have after 5 years?
Continuous compounding gives us principle function P(t) =
$1000 * e^(.08 t).
For t = 5 we have principle
- P(5) = $1000 * e^(.08 * 5) = $1489.82
The most basic exponential function forms are
The generalized forms for horizontal asymptote zero are
- y = A * 2^(kx)
- y = A * e^(kx)
- y = A * b^x.
Using the form y = A * b^x, assume that y = 20 when x = 5
and y = 30 when x = 12. Find the values of the parameters A and b.