How much money, invested at an interest rate of r % per year compounded continuously, will amount to A dollars after t years? (Round your answer to the nearest cent.)
A = 17,000, r = 4.3, t = 3

Question

How much money, invested at an interest rate of r % per year compounded continuously, will amount to A dollars after t years? (Round your answer to the nearest cent.)
A = 17,000,    r = 4.3,    t = 3

anonymous · Answer

A= Pe^rt right..?

anonymous · Answer

but how will i round it to the nearest cent..?

dumbcow · Answer

$$A = Pe^{rt}$$
solving for P
$$P = \frac{A}{e^{rt}}$$

yeah, plug in the values

anonymous · Answer

ow.. derive formula..

anonymous · Answer

so it is 14,942.55741 how will i round this to the nearest cent..?

dumbcow · Answer

round to 2 decimals

anonymous · Answer

ahhh.. tnx.. xDDDD

anonymous · Answer

wait

anonymous · Answer

Find the remainder r if the polynomial
4x^100 + 4x^85 − 4x^38 + 2x^17 − 6
divide by x+1
how can i find..?? will i input in the synthetic divison..  4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ..? up to the last to get the remainder..?

anonymous · Answer

or there is a shortcut..?

dumbcow · Answer

lol synthetic division is the short cut

dumbcow · Answer

crazy problem hope you have a lot of room

anonymous · Answer

yeah.. but 4x^100.. is so long to do..?

dumbcow · Answer

hold on, you just need the remainder right?

anonymous · Answer

yep.. just that crazy remainder.. hahah

dumbcow · Answer

then there is something called the remainder theorem :)

f(c) = remainder of dividing polynomial by (x-c)

so just plug in x = -1 to get remainder

anonymous · Answer

huh.. wait didnt get it..? i will just substitute it..?

dumbcow · Answer

yeah forget dividing , just evaluate at x=-1

anonymous · Answer

hwahha.. and then..? perform the equation after substituting..?

dumbcow · Answer

i could show the proof but im sure its in your textbook or notes somewhere

dumbcow · Answer

what do you get after substituting?

anonymous · Answer

the good news is maybe it is in somewhere in my notes or textbooks but the bad news is.. i forgot it in my locker at school... haha

anonymous · Answer

-12.. hwahah.. is that it..?

dumbcow · Answer

no worries http://en.wikipedia.org/wiki/Polynomial_remainder_theorem#Proof

dumbcow · Answer

yes its -12

anonymous · Answer

wow awesome.. thats cool.. its my first time to know that u can use the remainder thoerem at this one.. haha.. i got some tips now.. hwahah

dumbcow · Answer

:)

anonymous · Answer

last.. forgot to use the long division.. is synthetic only applicable if the x is single variable and has 1 exponent..?
Find the quotient and remainder if f(x) is divided by p(x).
f(x) = 3x^3 − 5x^2 − 4x − 12;    p(x) = 2x^2 + x

dumbcow · Answer

right it has to be in the form (x-c) to use synthetic division
so any x^2 will not work

dumbcow · Answer

hey if you need help with long division, here is a video https://www.khanacademy.org/math/algebra2/polynomial_and_rational/dividing_polynomials/v/dividing-polynomials-with-remainders its harder to help with long division using text

anonymous · Answer

yeah.. i guess haha.. because i can recall some steps but not all.. hahha

anonymous · Answer

tnx for the link..