Put n = 1 => A = P(1+i)^n = P(1+i)^1 = P(1+i)
You know that i = r/n => for n=1, i = r = interest rate
Remove the brackets and you'll have A = P + P*i
This equation looks like a linear equation. The variable of this equation is the interest rate or the initial amount P. In any case, the exponent of any of these variables is 1, therefore, the equation of final compounded amount is linear.
ANSWER: The equation A = P + P*i is linear.