document.write( "Question 1194927: find an exponential function of the form f(x) = ba^-x + c that has the horizontal asymptote y = 350 and y-intercept 70 and passes through the point (10,300). \n" ); document.write( "

Algebra.Com's Answer #827271 by greenestamps(13200) $\"\"$ $\"About$

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\n" ); document.write( " $\"f%28x%29=ba%5E%28-x%29%2Bc\"$

\n" ); document.write( "(1) For large values of x, a^(-x) goes to zero, so the function is $\"f%28x%29=c\"$ . The value of the function approaches 350 for very large values of x, so c=350. The function is

\n" ); document.write( " $\"f%28x%29=ba%5E%28-x%29%2B350\"$

\n" ); document.write( "(2) When x=0, a^(-x)=1, so the function is $\"f%28x%29=b%2B350\"$ . Since f(0)=70,

\n" ); document.write( " $\"b%2B350=70\"$
\n" ); document.write( " $\"b=-280\"$

\n" ); document.write( "The function is

\n" ); document.write( " $\"f%28x%29=-280a%5E%28-x%29%2B350\"$

\n" ); document.write( "(3) The function value is 300 when x=10.

\n" ); document.write( " $\"300=-280a%5E%28-10%29%2B350\"$
\n" ); document.write( " $\"280a%5E%28-10%29=50\"$
\n" ); document.write( " $\"a%5E%28-10%29=50%2F280=5%2F28\"$
\n" ); document.write( " $\"a%5E10=28%2F5=5.6\"$
\n" ); document.write( " $\"a=5.6%5E%281%2F10%29\"$ = 1.18800 to 5 decimal places.

\n" ); document.write( "ANSWER: The function is

\n" ); document.write( " $\"f%28x%29=-280%281.188%29%5E%28-x%29%2B350\"$

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