SOLUTION: Find the equation of the exponential curve with y-intercept of 3 and passing through point (3,192)

Algebra ->  Graphs -> SOLUTION: Find the equation of the exponential curve with y-intercept of 3 and passing through point (3,192)      Log On


   

Question 1008144: Find the equation of the exponential curve with y-intercept of 3 and passing through point (3,192)
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
( 3, 192 )
( 0, 3 )
+y+=+3%2Ae%5E%28k%2Ax%29+
-------------------
When +x=0+, +y+=+3+
+y+=+3%2Ae%5E0+
+y+=3+
That gives me the point ( 0,3 )
-------------------------
( 3, 192 )
+192+=+3%2Ae%5E%28+k%2A3+%29+
+e%5E%28+k%2A3+%29+=+64+
Take the natural log of both sides
+k%2A3+=+ln%28+64+%29+
+k+=+4.1589+%2F+3+
+k+=+1.3863+
----------------
The equation is:
+y+=+3%2Ae%5E%28+1.386x+%29+
Here's the plot:
+graph%28+400%2C+400%2C+-1%2C+5%2C+-10%2C+250%2C+3%2Ae%5E%28+1.386x+%29+%29+
Looks about right -hope I got it!