document.write( "Question 399595: rite an exponential function of the form y = ab^x whose graph passes thru the given points. (1,7), (2,49) \n" ); document.write( "

Algebra.Com's Answer #283163 by jsmallt9(3758) $\"\"$ $\"About$

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$\"y+=+ab%5Ex\"$
\n" ); document.write( "If the graph passes through the two given points then the coordinates of those points should fit the equation. So
\n" ); document.write( " $\"%287%29+=+ab%5E%28%281%29%29+=+ab\"$
\n" ); document.write( "and
\n" ); document.write( " $\"%2849%29+=+ab%5E%28%282%29%29+=+ab%5E2\"$
\n" ); document.write( "We now have two equations with two unknowns, a and b. We should be able to solve this system and find out what a and b are.

\n" ); document.write( "We can use the Substitution method. Solving the first equation for a we get:
\n" ); document.write( " $\"7%2Fb+=+a\"$
\n" ); document.write( "Substituting this into the second equation we get:
\n" ); document.write( " $\"49+=+%287%2Fb%29b%5E2\"$
\n" ); document.write( "which simplifies as follows:
\n" ); document.write( " $\"49+=+%287%2Fb%29%28b%5E2%2F1%29\"$
\n" ); document.write( " $\"49+=+7b%5E2%2Fb\"$
\n" ); document.write( "49 = 7b
\n" ); document.write( "Dividing by 7 we get:
\n" ); document.write( "7 = b
\n" ); document.write( "Using $\"7%2Fb+=+a\"$ and the value we just found for b, we can find a:
\n" ); document.write( " $\"7%2F%287%29+=+a\"$
\n" ); document.write( "1 = a
\n" ); document.write( "So a = 1 and b = 7. This makes the desired equation:
\n" ); document.write( " $\"y+=+%281%29%2A%287%29%5Ex\"$
\n" ); document.write( "or
\n" ); document.write( " $\"y+=+7%5Ex\"$ \n" ); document.write( "

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