SOLUTION: Find the equation for an exponential function that passes through the pair of points given below. (Round all coefficients to 4 decimal places when necessary.) Through (2, 36) and

Algebra ->  Exponents -> SOLUTION: Find the equation for an exponential function that passes through the pair of points given below. (Round all coefficients to 4 decimal places when necessary.) Through (2, 36) and       Log On


   

Question 1097432: Find the equation for an exponential function that passes through the pair of points given below. (Round all coefficients to 4 decimal places when necessary.)
Through (2, 36) and (4, 324)
Found 3 solutions by Fombitz, KMST, MathTherapy:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
y=ax%5Eb
.
.
(2,36)
36=a%282%5Eb%29
and
(4,324)
324=a%284%5Eb%29
So,
%28a%284%5Eb%29%29%2F%28a%282%5Eb%29%29=324%2F36
2%5Eb=9
b=log%282%2C%289%29%29
So then,
36=a%282%5Eb%29
36=a%282%5E%28log%282%2C%289%29%29%29%29
a=36%2F9
a=4
.
.
y=4x%5E%28log%289%2C%282%29%29%29
.

Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
Let the exponential function be
f%28x%29=A%2Ab%5Ex , with b%3E0 .
We know that
f%282%29=A%2Ab%5E2=36
f%284%29=A%2Ab%5E4=324
So,
A%2Ab%5E4%2F%28A%2Ab%5E2%29=324%2F36 --> b%5E2=9 --> b=3 .
Substituting the value found for b into A%2Ab%5E2=36 ,
we get A%2A3%5E2=36 --> A%2A9=36 --> A=36%2F9 --> A=4 .
The function is
highlight%28f%28x%29=4%2A3%5Ex%29 .

Answer by MathTherapy(10555) About Me  (Show Source):
You can put this solution on YOUR website!

Find the equation for an exponential function that passes through the pair of points given below. (Round all coefficients to 4 decimal places when necessary.)
Through (2, 36) and (4, 324)
Correct exponential-function equation: matrix%281%2C3%2C+y%2C+%22=%22%2C+ab%5Ex%29

Substituting the coordinates in the above equation, you'll get the values of a and b.

You should get: