A dog takes 465 mg of Rimadyl. Each hour, the amount of Rimadyl in a dog's system decreases by about $29 \%$. Assume that the exponential decay of Rimadyl in the dog's system can be model as $f(x)=a(1-r)^{z}$ where a is the initial dose, $r$ is the rate of decay and $x$ is the number of hours. How much Rimadyl is left in the system after 6 hours? Round your answer to the nearest hundredths.

Step 1 ：Given that the initial dose of Rimadyl is \(a = 465\) mg, the rate of decay is \(r = 0.29\), and the time is \(x = 6\) hours.

Step 2 ：The exponential decay model is given by \(f(x)=a(1-r)^{x}\).

Step 3 ：Substitute the given values into the formula: \(f(6) = 465(1-0.29)^{6}\).

Step 4 ：Calculate the expression inside the parentheses: \(1 - 0.29 = 0.71\).

Step 5 ：So, the equation becomes: \(f(6) = 465(0.71)^{6}\).

Step 6 ：Calculate the power: \((0.71)^{6} \approx 0.05042061\).

Step 7 ：So, the equation becomes: \(f(6) = 465 * 0.05042061\).

Step 8 ：Calculate the multiplication: \(f(6) \approx 23.44538\).

Step 9 ：So, after 6 hours, there is approximately 23.45 mg of Rimadyl left in the dog's system, rounded to the nearest hundredths.

Step 10 ：Finally, check the result. The amount of Rimadyl in the system decreases each hour, so the amount after 6 hours should be less than the initial dose. Our result is indeed less than 465 mg, so it seems reasonable.

Step 11 ：\(\boxed{23.45}\) mg of Rimadyl is left in the dog's system after 6 hours.