2023 YTSS P2 Q4

A potato field is infested by insects. The percentage of the field that is infested, \(q\%\), \(t\) days after pesticide is sprayed is modelled by the equation \[\dfrac{\mathrm dq}{\mathrm dt}=-\dfrac5{\sqrt{(2t+1)^3}}.\]

Just before the pesticide is sprayed, \(5\%\) of the field was already infested with insects. Once the percentage of the field that is infested decreases to \(1\%\) or less, the potatoes will be harvested. Find the minimum number of days for the potatoes to be harvested.[5]