SOLUTION: Find a formula for the exponential function passing through the points (-1,3/5) and (3,375).

Algebra ->  Exponents -> SOLUTION: Find a formula for the exponential function passing through the points (-1,3/5) and (3,375).      Log On


   

Question 1148671: Find a formula for the exponential function passing through the points (-1,3/5) and (3,375).
Found 3 solutions by josmiceli, MathTherapy, greenestamps:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+y+=+a%2Ab%5Ex+
( -1, 3/5 )
( 3, 375 )
----------------
+3%2F5+=+a%2Ab%5E%28-1%29+
+a%2Fb+=+3%2F5+
----------------------
+375+=+a%2Ab%5E3+
+a+=+375%2Fb%5E3+
----------------------
+375%2Fb%5E4+=+3%2F5+
+3%2Ab%5E4+=+5%2A375+
+b%5E4+=+1875+
+b+=+6.5804+
+a+=+%283%2F5%29%2Ab+
+a+=+.6%2A6.5804+
+a+=+3.94822+
-----------------------
+y+=+3.94822%2A6.5804%5Ex+
---------------------------------
Check:
+.6+=++3.94822%2A6.5804%5E%28-1%29+
+.6+=+.6+
You can check the other point


Answer by MathTherapy(10555) About Me  (Show Source):
You can put this solution on YOUR website!
Find a formula for the exponential function passing through the points (-1,3/5) and (3,375).
The other person's answer is WRONG!
matrix%281%2C3%2C+y%2C+%22=%22%2C+ab%5Ex%29
matrix%281%2C3%2C+3%2F5%2C+%22=%22%2C+ab%5E%28-+1%29%29 ------ Substituting (- 1, 3%2F5) for (x, y)
 ------- eq (i)


matrix%281%2C3%2C+y%2C+%22=%22%2C+ab%5Ex%29
matrix%281%2C3%2C+375%2C+%22=%22%2C+ab%5E3%29 ----- Substituting (3, 375) for (x, y)
matrix%281%2C3%2C+a%2C+%22=%22%2C+375%2Fb%5E3%29 ------- eq (ii)


This then results in: matrix%281%2C3%2C+3b%2F5%2C+%22=%22%2C+375%2Fb%5E3%29
matrix%281%2C3%2C+3b%5E4%2C+%22=%22%2C+5%28375%29%29------- Cross-multiplying
matrix%281%2C5%2C+b%5E4%2C+%22=%22%2C+5%28375%29%2F3%2C+%22=%22%2C+625%29
matrix%281%2C5%2C+b%2C+%22=%22%2C+root+%284%2C+625%29%2C+%22=%22%2C+5%29
matrix%281%2C5%2C+a%2C+%22=%22%2C+3%285%29%2F5%2C+%22=%22%2C+3%29 ------- Substituting 5 for b in eq (i)
Exponential function: highlight_green%28matrix%281%2C3%2C+f%28x%29%2C+%22=%22%2C+3%285%29%5Ex%29%29

Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


Substitute the two given points into the general formula for an exponential function,

y+=+a%2Ab%5Ex

(1) 3%2F5+=+a%2Ab%5E%28-1%29
(2) 375+=+a%2Ab%5E3

Divide (2) by (1):

375%2F%283%2F5%29+=+%28ab%5E3%29%2Fab%5E%28-1%29
625+=+b%5E4

b+=+5

Use that value of b in one of the original equation to determine the value of a.

375+=+a%2A5%5E3+=+125a
a+=+3

ANSWER: The function is y+=+3%2A%285%5Ex%29