Question 22642
{{{3000=2000(1+.06)^t}}}


Divide both sides by 2000:
{{{3000/2000 =(2000(1+.06)^t)/2000}}}

{{{3/2 = 1.06^t}}}


In order to solve for t, where t is an exponent, you must take the ln of each side of the equation.  It also works to take the log of each side--exactly the same answer!

{{{ln (3/2) = ln (1.06^t) }}}


This should bring back the laws of logarithms, in which the exponent becomes the coefficient:

{{{ln(3/2) = t*ln(1.06) }}}


Finally divide both sides by ln(1.06), and calculate with a calculator:

{{{t= (ln(3/2))/(ln(1.06)) }}}= 6.958515, which rounds off to about 6.96.


R^2 at SCC