Find the logarithmic derivative and then determine the percentage rate of change of the function at the points indicated.
\[
f(t)=7 t^{6} \text { at } t=20 \text { and } t=50
\]

Step 1 ：Given the function \(f(t)=7 t^{6}\) at \(t=20\) and \(t=50\)

Step 2 ：First, find the derivative of the function, \(f'(t)\)

Step 3 ：\(f'(t) = 42t^{5}\)

Step 4 ：Then, find the logarithmic derivative at the given points using the formula \(\frac{f'(t)}{f(t)}\)

Step 5 ：At \(t=20\), the logarithmic derivative is \(\frac{3}{10}\)

Step 6 ：At \(t=50\), the logarithmic derivative is \(\frac{3}{25}\)

Step 7 ：Finally, find the percentage rate of change at the given points using the formula \(\frac{f'(t)}{f(t)} \times 100\%\)

Step 8 ：At \(t=20\), the percentage rate of change is \(30\%\)

Step 9 ：At \(t=50\), the percentage rate of change is \(12\%\)

Step 10 ：Final Answer: The percentage rate of change of the function at \(t=20\) is \(\boxed{30\%}\) and at \(t=50\) is \(\boxed{12\%}\)