write the equation for an exponential function, in the form y=a*b^2, whose graph passes through the coordinate points (1,7.5) and (3,16.875)
To find the equation of the exponential function, we can use the two coordinate points given:
(1, 7.5) --> y = a * b^1
(3, 16.875) --> y = a * b^3
Using the first point:
7.5 = a * b
Using the second point:
16.875 = a * b^3
We can divide the second equation by the first equation to eliminate 'a':
16.875 / 7.5 = b^3 / b
2.25 = b^2
Now that we have found the value of 'b', we can substitute it back into the first equation to find the value of 'a':
7.5 = a * 2.25
a = 7.5 / 2.25
a = 3.33333333
Therefore, the equation of the exponential function passing through the given points is:
y = 3.33333333 * 2.25^x