Cool problem. We need 2 equations using the 2 given points (4,4) and (16.8)
4 = ab^4. Equation #1
8 = ab^16 Equation #2
Divide equation 1 by equation2. 8/4 = Ab^16/Ab^4
This gives us 2 = b^12. Note that the a’s cancel out
b= 2^1/12 ( b = the 12th root of 2 or 2 raised to the 1/12th power
Now that we have b lets go back to equation #1 4 = a(2^1/12)^4 ( we have substituted 2^1/12 for b)
4 = a(2^1/3) ( when we take a power to a power we multiply (1/12) x4 =4/12 or 1/3
solving for a a= 4/ 2^1/3. A=2^2/2^1/3. So a = 2^5/3
Equation is y= (2^5/3) x (2^1/2)^x
Graph this equation and you will see that the 2 given points fall on the graph
Stephen K.
03/21/19