Question

Equation too big for Wolfram Alpha, can someone help me solve this.

10000=100*(1+r+r^2+r^3+r^4+r^5+r^6+r^7+r^8+r^9+r^10+r^11+r^12+r^13+r^14+r^15+r^16+r^17+r^18+r^19+r^20+r^21+r^22+r^23+r^24+r^25+r^26+r^27+r^28+r^29+r^30+r^31+r^32+r^33+r^34+r^35+r^36+r^37+r^38+r^39+r^40)

Where r = e^(-0.00479t)
Solve for t
My calculator came up with -8, which can't be right.

Answer 1

try the sum of a geometric series

Answer 2

\[100\frac{1-r^n}{1-r}\]

Answer 3

n=39 it looks like

Answer 4

or 40

Answer 5

40

Answer 6

Trying that method on my calculator

Answer 7

S = 1+r+r^2
-r S = -r-r^2-r^3
-----------------
1-rS = 1 - r^3


S = 1-r^3/1-r

use r^41 in this

Answer 8

10000(1-e^(-0.00479t))/100 = 1-e^41*(-0.00479t)

100(1-e^(-0.00479t)) = 1-e^41*(-0.00479t)

99 = -e^41*(-0.00479t)+100e^(-0.00479t))

99 = -e^41*(-0.00479t)+100e^(-0.00479t))

etc...

Answer 9

Calculator still calculating

Answer 10

i get t = -8.202... and 0; but zero is superfluous

Answer 11

Hmmm, I must have made a mistake somewhere. I'll ask a classmate. Thanks a lot for your help

Answer 12

yw