document.write( "Question 108088: So lost can anyone help me? find k in the exponential function
\n" ); document.write( " N(t)=N base0e^kt, given that N(0)=1 and N(3)=7. thanks in advance. \n" ); document.write( "

Algebra.Com's Answer #78826 by Fombitz(32388) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"N%28t%29=N%5B0%5De%5Ekt\"$ where
\n" ); document.write( "N(0)=1 and N(3)=7
\n" ); document.write( "Use your two values to solve for $\"k\"$ and $\"N%5B0%5D\"$
\n" ); document.write( " $\"N%28t%29=1\"$
\n" ); document.write( " $\"N%280%29=1\"$
\n" ); document.write( " $\"N%5B0%5De%5E%28k%2A0%29=1\"$
\n" ); document.write( " $\"N%5B0%5D%2A1=1\"$
\n" ); document.write( " $\"N%5B0%5D=1\"$
\n" ); document.write( " $\"N%28t%29=N%5B0%5De%5Ekt\"$
\n" ); document.write( " $\"N%283%29=7\"$
\n" ); document.write( " $\"N%5B0%5De%5Ek%283%29=7\"$
\n" ); document.write( " $\"1%2Ae%5Ek%283%29=7\"$
\n" ); document.write( " $\"e%5Ek%283%29=7\"$
\n" ); document.write( " $\"k%283%29=ln%287%29\"$
\n" ); document.write( " $\"k=ln%287%29%2F3\"$
\n" ); document.write( "k~0.649
\n" ); document.write( "Check your answers.
\n" ); document.write( " $\"N%28t%29=e%5E0.649t\"$
\n" ); document.write( " $\"N%280%29=e%5E0.649%280%29\"$
\n" ); document.write( " $\"N%280%29=1\"$
\n" ); document.write( " $\"N%283%29=e%5E0.649%283%29\"$
\n" ); document.write( " $\"N%283%29=e%5E1.947\"$
\n" ); document.write( " $\"N%283%29=7.0\"$
\n" ); document.write( "These values match your original values.
\n" ); document.write( " $\"N%5B0%5D=1\"$
\n" ); document.write( " $\"k=ln%287%29%2F3\"$ \n" ); document.write( "

\n" );