SOLUTION: How do you write (0,0.5) (1,3) as an exponential function?

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Question 258412: How do you write (0,0.5) (1,3) as an exponential function?
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
Exponential functions have equations in the following form:
y+=+k%2Aa%5Ex
(Your book/teacher may use letters other than k and a but the basic form should be the same.)
With the two ordered pairs we have two sets of x and y values that should fit the equation:
0.5+=+k%2Aa%5E0 and 3+=+k%2Aa%5E1
We can use this system to solve for k and a. The first equation, since anything but zero to the zero power is a 1, simplifies to:
0.5+=+k%2A1
or
0.5+=+k
Already we have the k for our function. Now we can use this value for k and the second equation to find a:
3+=+%280.5%29a%5E1
Since a%5E1+=+a:
3+=+%280.5%29a
Multiplying both sides by 2 we get:
6+=+a
With k = 0.5 and a = 6 our exponential function is:
y+=+%280.5%296%5Ex