A population of 530 bacteria is introduced into a culture and grows in number according to the equation below, where t is measured in hours. Find the rate at which the population is growing (in bacteria/hour) when t = 5. (Round your answer to two decimal places. ) P(t) = 530(1 + 5t 40 + t2) P′(5) = bacteria/hour bacteria/hour
![The displacement (in centimeters) of a particle s moving back and forth along a straight line is given by the equation s = 2 sin(πt) + 4 cos(πt), where t is measured in seconds. (Round your answers to two decimal places. ) (a) Find the average velocity during each time period. (i) [1, 2] cm/s (ii) [1, 1.1] cm/s (iii) [1, 1.01] cm/s (iv) [1, 1.001] cm/s (b) Estimate the instantaneous velocity of the particle when t = 1. cm/s](https://www.doubtrix.com/uploads/editor/9947714394TPgahcSJtp.png)