SOLUTION: Find a formula for the exponential function passing through the points (-3,2/9) and (2,18)

Algebra ->  Exponents -> SOLUTION: Find a formula for the exponential function passing through the points (-3,2/9) and (2,18)      Log On


   

Question 1148726: Find a formula for the exponential function passing through the points (-3,2/9) and (2,18)
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+y+=+a%2Ab%5Ex+
( -3, 2/9 )
+2%2F9+=+a%2Ab%5E%28-3%29+
+a+=+%282%2F9%29%2Ab%5E3+
-----------------------
( 2, 18 )
+18+=+a%2Ab%5E2+
+18+=+%282%2F9%29%2Ab%5E3%2Ab%5E2+
+%289%2F2%29%2A18+=+b%5E5+
+b%5E5+=+81+
+b%5E5+=+3%5E4+
+b+=+3%5E%284%2F5%29+
and
+a+=+%282%2F9%29%2Ab%5E3+
+a+=+%282%2F9%29%2A3%5E%2812%2F5%29+
---------------------------
+y+=++%282%2F9%29%2A3%5E%2812%2F5%29%2A3%5E%28%28+%284%2F5%29%2Ax+%29%29+
+y+=+%282%2F9%29%2A3%5E%28%28+12%2F5+%2B+%284%2F5%29%2Ax+%29%29+
----------------------------------------
check:
( -3, 2/9 )
+y+=+%282%2F9%29%2A3%5E%28+12%2F5+%2B+%284%2F5%29%2Ax+%29+
+2%2F9+=+%282%2F9%29%2A3%5E%28%28+12%2F5+%2B+%284%2F5%29%2A%28-3%29+%29%29+
+2%2F9+=+%282%2F9%29%2A3%5E0+
+2%2F9+=+2%2F9+
OK
( 2, 18 )
+y+=+%282%2F9%29%2A3%5E%28+12%2F5+%2B+%284%2F5%29%2Ax+%29+
+18+=+%282%2F9%29%2A3%5E%28+12%2F5+%2B+%284%2F5%29%2A2+%29+
+81+=+3%5E%28%28+12%2F5+%2B+%284%2F5%29%2A2+%29%29+
+81+=+3%5E%28+20%2F5+%29+
+81+=+3%5E4+
+81+=+81+
OK
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