document.write( "Question 1008144: Find the equation of the exponential curve with y-intercept of 3 and passing through point (3,192) \n" ); document.write( "

Algebra.Com's Answer #623916 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
( 3, 192 )
\n" ); document.write( "( 0, 3 )
\n" ); document.write( " $\"+y+=+3%2Ae%5E%28k%2Ax%29+\"$
\n" ); document.write( "-------------------
\n" ); document.write( "When $\"+x=0+\"$ , $\"+y+=+3+\"$
\n" ); document.write( " $\"+y+=+3%2Ae%5E0+\"$
\n" ); document.write( " $\"+y+=3+\"$
\n" ); document.write( "That gives me the point ( 0,3 )
\n" ); document.write( "-------------------------
\n" ); document.write( "( 3, 192 )
\n" ); document.write( " $\"+192+=+3%2Ae%5E%28+k%2A3+%29+\"$
\n" ); document.write( " $\"+e%5E%28+k%2A3+%29+=+64+\"$
\n" ); document.write( "Take the natural log of both sides
\n" ); document.write( " $\"+k%2A3+=+ln%28+64+%29+\"$
\n" ); document.write( " $\"+k+=+4.1589+%2F+3+\"$
\n" ); document.write( " $\"+k+=+1.3863+\"$
\n" ); document.write( "----------------
\n" ); document.write( "The equation is:
\n" ); document.write( " $\"+y+=+3%2Ae%5E%28+1.386x+%29+\"$
\n" ); document.write( "Here's the plot:
\n" ); document.write( " $\"+graph%28+400%2C+400%2C+-1%2C+5%2C+-10%2C+250%2C+3%2Ae%5E%28+1.386x+%29+%29+\"$
\n" ); document.write( "Looks about right -hope I got it! \n" ); document.write( "

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