6. The population of a slowly growing bacterial colony after thours is given by p(t)=5t^2+30t+100 Find the growth rate after 4 hours. Answer: square .

To find the growth rate of the bacterial colony after 4 hours, we need to find the derivative of the population function $p(t)$ with respect to time $t$. The derivative represents the rate of change of the population with respect to time, which is the growth rate.<br /><br />Given the population function:<br />\[ p(t) = 5t^2 + 30t + 100 \]<br /><br />We need to find the derivative $p'(t)$:<br />\[ p'(t) = \frac{d}{dt}(5t^2 + 30t + 100) \]<br /><br />Using the power rule for differentiation, we get:<br />\[ p'(t) = 10t + 30 \]<br /><br />Now, we need to evaluate the derivative at $t = 4$ to find the growth rate after 4 hours:<br />\[ p'(4) = 10(4) + 30 \]<br />\[ p'(4) = 40 + 30 \]<br />\[ p'(4) = 70 \]<br /><br />Therefore, the growth rate of the bacterial colony after 4 hours is $\boxed{70}$.