document.write( "Question 258412: How do you write (0,0.5) (1,3) as an exponential function? \n" ); document.write( "

Algebra.Com's Answer #190334 by jsmallt9(3758) $\"\"$ $\"About$

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Exponential functions have equations in the following form:
\n" ); document.write( " $\"y+=+k%2Aa%5Ex\"$
\n" ); document.write( "(Your book/teacher may use letters other than k and a but the basic form should be the same.)
\n" ); document.write( "With the two ordered pairs we have two sets of x and y values that should fit the equation:
\n" ); document.write( " $\"0.5+=+k%2Aa%5E0\"$ and $\"3+=+k%2Aa%5E1\"$
\n" ); document.write( "We can use this system to solve for k and a. The first equation, since anything but zero to the zero power is a 1, simplifies to:
\n" ); document.write( " $\"0.5+=+k%2A1\"$
\n" ); document.write( "or
\n" ); document.write( " $\"0.5+=+k\"$
\n" ); document.write( "Already we have the k for our function. Now we can use this value for k and the second equation to find a:
\n" ); document.write( " $\"3+=+%280.5%29a%5E1\"$
\n" ); document.write( "Since $\"a%5E1+=+a\"$ :
\n" ); document.write( " $\"3+=+%280.5%29a\"$
\n" ); document.write( "Multiplying both sides by 2 we get:
\n" ); document.write( " $\"6+=+a\"$
\n" ); document.write( "With k = 0.5 and a = 6 our exponential function is:
\n" ); document.write( " $\"y+=+%280.5%296%5Ex\"$ \n" ); document.write( "

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