Rate of reaction increases exponentially with concentration In our chemistry practical we dropped 0.07g of Magnesium into various concentrations of an acid (sulfuric or hydrochloric - only one was used, not sure which), and measured the rate of reaction by the rate of the H2 produced (used a gas syringe). We then collected data at a suitable interval of the culmulative amount of H2 produced.
We drew the graph (with multiple concentrations - 0.25, 05, 0.75, 1, 2). Then we measured the steepest point (fastest rate) and took the gradient. 
Plotting rate against concentrations (0.25, 05, 0.75, 1, 2), we came to the conclusion that rate varies exponentially with concentration. 
But the rate law of a typical reaction is:

r = k * [A] * [B]


, which would mean doubling [B] would double the rate law, not have an exponential effect on the reaction. Why did we come to the conclusion that concentration has an exponential effect?

In our case the rate law, I would think, would be elementary, but we are not dealing with concentrations of both Mg and HCl, just HCl, as the Mg was solid - therefore no concentration of Mg in solution.

My question is: In a reaction between two liquids, is the rate of reaction linearly dependent on the concentration?
AND: What is the rate law of our reaction? - Why did we come to the conclusion we did?

Thanks for the help!! :)
Rate equation is experimentally determined. So, you can't directly write $r=k[A][B]$ (where r is rate, k is rate constant). Probably you might have performed first order reaction. For which $r=k[A]=\frac{2.303}{t}log\frac{[R]}{[R_0]}=\frac{2.303}{t}log{e^{kt}}$.   

The above equation suggests that rate is proportional to exponential function.