Final answer:
To write an exponential function that contains the points (4,27) and (2,3), substitute the coordinates into the general form of an exponential function to get two equations. Divide the equations to eliminate the variable 'a' and solve for 'b'.
Step-by-step explanation:
To write an exponential function that contains the points (4,27) and (2,3), we can use the general form of an exponential function, which is y = ab^x. Substitute the coordinates of each point into the equation to get two equations:
27 = ab^4
3 = ab^2
Now divide these equations to eliminate the variable 'a':
(27/3) = (ab^4)/(ab^2)
9 = b^2
Take the square root of both sides to solve for 'b':
b = ±3
Now substitute the value of 'b' back into one of the original equations to solve for 'a':
3 = a(±3)^2
3 = 9a
a = 3/9 = 1/3
Therefore, the exponential function that contains the points (4,27) and (2,3) is y = (1/3)(3)^x.