Tuesday, November 13, 2007

Scribe Post - Logs and Exponents

Today we start off with some review on logs and exponents:





looking at 19^(x-5)=3^(x+2) we know that to get an exact answer we must get the log of both sides..

which then becomes: Log19^(x-5)=Log3^(x+2)


REMEMBER: That Log is an exponent



so when an exponent is increasing to another exponent we can multiply them:
which we can then expand and move x to one side which becomes:

now something a little new....

well first what is compound interest?

compound interest is growth from the original amount by a certain rate that will continue to grow exponentially from the last amount

we were given a formula that can help us calculate this value:

A = The new Amount
P = Principal/original amount
R = The rate of which it will accumulate
N = Number of times per time amount given (rate will be divided by this value)
T = Amount of Time that it has been accumulating for (yearly, seconds, months, whatever it may be)




knowing that we can plug in what ever information is given to find what we need to know:



we see that that question sayes "How much money will you have after 5 years if you invested $300" "5 years" becomes our T value and "$300" becomes our P value


then its goes to say"at 6% interest compounded annually? monthly?"

T=5

P=300
well r=0.06 (6%)

n=1 annually means yearly

n also will = 12 (monthly)


which means you have use this formula twice to get a monthly and yearly amount

now when this interest is compounded continuously we would use a different formula but will look very much the same:

and so in this next question we can see how we would use it.


first question is pretty straight forward, much like the last one we did only difference is that it is compounded continuously. Sooo p=300 r=0.06 t=5


the second question ask if you made if you have invested $300(P=300) at 6%(r=0.06) how long will it take to get double your money (A=600). so it wants to no T time it will take to get $600
600 and 300 will reduce to 2 and 1:
2 = e^0.06t
if we take the ln (log e log base e) of both sides then divide by 0.06 we can isolate t
ln2=lne^0.06t

ln2 =0.06t
0.06 0.06

ln2 = t
0.06


that's about all we learn in the morning in the afternoon we had a short log quiz and then we did exercise the next for the rest of the class time


The Next Scribe Isssssssssssss..................... not lina as i said before, but instead will

be luis voluntarily.

sorry for the mix up i was in a bit of a rush

4 comments:

lina said...

Good scribe Joe. You explained today's class well. Good use of colour too, very stimulating.
I just wanted to say that I already scribed for Friday though. =)

JoeS said...

yeah sorry about that but i fix it luis will be doing the next scribe

SAMUS said...

GREAT SCRIBE! i understood what was going on and i understand the change of base law completely. HALL OF FAME!

GOAT said...

hall of fame baby!