The exponential function g g, represented in the table, can be written as g ( x ) = a ⋅ b x g(x)=a⋅b x . x x g ( x ) g(x) 0 0 1 2 12 1 1 2 2 complete the equation for g ( x ) g(x).

Ok, so the function form is y = a * bx.

Substitute in the values:

750 = a * b5

and

48 = a * b2

Then divide the two equations:

750/ 48 = (a * b5) / (a * b2)

So:  

15.625 = b3

Take the cube root of both sides:

2.5 = b

Now, substitue b into one of the equations (the one with 48 has smaller numbers and is easier to work with.)

48 = a * 2.52

Simplify.

48 = a * 6.25

Divide both sides by 6.25

7.68 = a

Now substitute in a and b to write the exponential function:  

y = 7.68 * 2.5x

Step-by-step explanation:

because linear equations are a lot simpler than quadratics equations, and linear equations formula is a lot easier to memorize. that's why i think they're harder.