Consider the initial value problem 25y′′+40y′+16y=0, y(0)=a, y′(0)=−1. Find the critical value of a that separates solutions that become negative from those that are always positive for t>0.

Aculture started with 3000 bacteria. after 5 hours it grew to 3900 bacteria. predict how many bacteria will be present after 9 hours

How can you tell when x and y are not directly proportional?

The position of a moving particle is given by the position function: f(t)=-9t-t^2-0.2t^3+0.1t^4 0 a. at what time does the particle reverse direction? b. when is the displacement positive? (round one decimal place and answer in interval notation) c. when is the displacement negative? (round one decimal place and answer in interval notation) d. when is the particle’s acceleration positive? (round one decimal place and answer in interval notation) e. when is the particle’s acceleration negative? (round one decimal place and answer in interval notation)