SOLUTION: Find a formula for the exponential function passing through the points (-3,4/27) and (2, 36)

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Find a formula for the exponential function passing through the points (-3,4/27) and (2, 36)       Log On


   

Question 916449: Find a formula for the exponential function passing through the points (-3,4/27) and (2, 36)
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

Find a formula for the exponential function passing through the points (-3,4%2F27) and (2, 36)
The exponential form is:
y+=+a%28b%5Ex%29
Putting (-3, 4%2F27) in for x and y, you get this:
4%2F27+=+a%28b%5E-3%29 ........ solve for "b"
4%2F27+=+a%281%2Fb%5E3%29

4%2F27a+=+%281%2Fb%5E3%29
4b%5E3+=+27a
b%5E3+=+27a%2F4
b+=root%283%2C+3%5E3a%2F4%29
b+=3root%283%2C+a%2F4%29
Putting (2,36) in for x and y, you get this:
36=+a%28b%5E2%29

36=a%2A%283root%283%2C+a%2F4%29%29%5E2
36=9a%2A%28root%283%2C+a%2F4%29%29%5E2 => highlight%28a=4%29

Now substitute "a" in "b+=3root%283%2C+a%2F4%29" and find "b":
b+=3root%283%2C+4%2F4%29
b+=3root%283%2C+1%29
highlight%28b+=3%29
The final equation becomes:
highlight%28y+=+4%283%5Ex%29%29+
check given points:
(-3,4%2F27) and (2, 36)
36+=+4%283%5E2%29+
36+=+4%289%29+
36+=+36+

4%2F27=4%283%5E-3%29
4%2F27=4%281%2F3%5E3%29
4%2F27=4%281%2F27%29
4%2F27=4%2F27