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225 is a constant, you can pull that aside and focus on 1.15^t

ln1.15(x) = t try to substitute that

not ln...but log1.15(x) = t

why did you take though

log ...im sorry

just thought itd be easier to play with.... I got no objection to another way :)

oh ok...is there a general pattern that i should follow...or even an order

i think I recall the base other than e stuff now...

1.15^t is the derivative of some F(x) what do we know about exponent derivatives?

OMG im so confused

Dx(5^x) = Dx 5^x right? or am i forgetting something there...which I am prone to do

you want to integrate this function right?

yea

oh ok

we dont want to change any value to it, just the way it "looks"

alright... so its log 1.15(x)= t {where did u get x from}

lol..ok

y = 5^x how would we "derive" this? do you recall?

lnx (5^x)

you sure? cause it looks right to me...

haha.. i think ...wait let me check

remember the steps to get it?

what steps?

it actually is ln(5) 5^x

thats better :)

so damn close

ok..now were ready lol

thanks for not bailing on me half way

so the derivative of 5^t would be?

i got nowhere to go ....

ln(5)5^t

and that is our "key" to this problem

14 times what = 14?

*1

omg...idk

lol ..... what do you know that equals 1?

does 4/2 = 1?
does 4/3 =1?
does 4/4 =1??

ohhh ....4/4?

instead of a "4" we need what..... ln(1.15) right?

yea

good, lets set up out integrand then...

this is our starting point
\[\int\limits_{} 225(1.15^t)\]

dont we have to use F(b)-F(a)

lets pull out the constants to get this:\[225 \int\limits_{} 1.15^t\]

we need to find F(x) before we can use it lol

dang it

now lets multiply our integrand by our convenient form of "1"

\[225 \int\limits_{} [\ln(1.15)/\ln(1.15)] 1.15^t\]

tell me... is ln(1.15) a constant??

yes

then lets pull the bottom one out and leave the top in to use..sound good?

\[225/\ln(1.15) \int\limits_{} \ln(1.15) 1.15^t\]

okay that kinda makes sense

now what do we know our integrand will become?

oh shoot ......1.15^t

thats correct :)
\[F(t) = [225/\ln(1.15)] 1.15^t \]

now use your "t" values and figure out the answer :)

ok...i had one more question....so my values are gonna 1 and 28?

225
------- * 1.15^t = F(t)
ln(1.15)

id subtract 1965 from both years to get a span of time

yeah i subtracted 1965 from 1983

1983?? or 1993?

1993...my bad

it aint 1 to 28, its.... zero to 28. 1965-1965=0

thats where i was confused .

1.15^0 = 1 so that aint a biggy

yeah....it was the subtraction that confused ya :) lol

OMG...i got it right...THANK YOU

80599.643 - 1609.88 =?

yay!!! that means im smart ;)

we..were smart

yea...u my friend are the man...

just dont ask me the hard questions :)

lol...its all good