Question

Please read my replies after as well:

(a) Suppose on Jan 1, 1997 Dave invested $2,000 into a bank account at 5% interest compounded continuously. Let y(t) be the value of Dave's investment after t years. Give an exact formula for y(t)
(b) Also on Jan 1, 1997 John decides to invest. He put $2,500 into an account at 3% interest compounded monthly. Let g(t) be the value of John's investment after t years. Give an exact formula for g(t).
(c) Which account is worth more after 9 years? [ Must show work to receive credit.]
(d) To the nearest tenth, at what time t is the value of both accounts the same?

Answer 1

I have the answers too everything except D, i dont understand why i cant get it

Answer 2

a) y(t) = 2000e^.05t
b) g(t) = 2500(1+.03/12)^12t
c) g(t) is larger
d) ???

Answer 3

i set the 2 equations equal to each other, but i cannot isolate t... not sure if im doing it wrong or idk lol help?

Answer 4

what do you mean? that would give me the answer to c, 3136.62 and 3273.81

Answer 5

yeah, thats the one i can not get any thoughts?

Answer 6

what i did was
2000e^.05t = 2500 (1+.03/12)^12(t)

i set them equal to each other because if im trying to find when they both give the same answer, that means they themselves are equal.. but i cant find a way to isolate T in order to find how long it takes

Answer 7

yeah i got to that part too... took the ln of both sides and got that, but still can't isolate the t to find what it's worth. where do i go from there?

Answer 8

wait what happened to the 1.0025?

Answer 9

sorry i still dont see how that brings me to the answer, the answer rounded should come out to 11.1

Answer 10

lol alright let me know what you come up with

Answer 11

anything?

Answer 12

sigh =(.. this is ridiculous. but im right in setting the equations equal to each other right?

Answer 13

You're absolutely right!

Answer 14

this is really frustrating... thank you for your help tho, i hope its something wrong with the problem lol

Answer 15

thank you, sorry for having you spend all that time on me

Answer 16

e^.05t = 1.25 ( 1.0025 )^ 12t
.05t = ln 1.25 + 12 ln ( 1.0025 ) t
.[ 05 - 12 ln ( 1.0025) ] t = ln 1.25
=> t = 11.136

Answer 17

Finally, I found my flaw =)

Answer 18

how did the addition sign come along?

Answer 19

ln ( xy) = ln x + lny

Answer 20

oh wow dude you're a boss. how did i not think of that -__-... thanks a lot man haha much appreciated

Answer 21

lol i could imagine its 3 am and i have this final tomorrow at 4 haha

Answer 22

Rutgers university?

Answer 23

or do you mean time wise? lol

Answer 24

oh haha yeah jersey strong =P

Answer 25

i actually do have a problem i dont understand, i need to figure out how to show you the graph tho, let me see if i can save the picture

Answer 26

Open the new post to attract more help :)

Answer 27

lol alright

Answer 28

woop, thats the entire exam review, its number 25 lol