Paramter interpretation with scaled data

Questions v5
3

Thank you for the detailed explanation.
What is the difference between using pm.math and basic python math then?

For example:
1)

def fn(a,b,c,x):
    y_hat = a + b*x + x**c
    y_hat = np.exp(y_hat)
    return y_hat

y_hat = fn(a,b,c,x)

vs
2)

def fn(a,b,c,x):
    
    y_hat = a + b*x + x**c
    return y_hat

y_hat = fn(a,b,c,x)
y_hat = pm.math.exp(y_hat)

Would result in any differences?