The spread of a disease through a community can be modeled with the logistic equation dy/dt = 0.9/1+45eˉ⁰·¹⁵ᵗ , where y is the proportion of people infected after t days . according to the model, what percentage of the people in the community will not become infected? (a) 2% (b) 10% (c) 15% (d) 45% (e) 90%

Imagine a new pasture with grass growing on it. every day after the seeds have germinated, the number of blades of grass in the pasture triples. after 18 days, the entire pasture is completely covered in grass. how many days did it take for the pasture to be one-third covered in grass?

Select all of the quadrants that the parabola whose equation is y=√x-4 (principal square root) occupies. i ii iii iv

Prove (a) cosh2(x) − sinh2(x) = 1 and (b) 1 − tanh 2(x) = sech 2(x). solution (a) cosh2(x) − sinh2(x) = ex + e−x 2 2 − 2 = e2x + 2 + e−2x 4 − = 4 = . (b) we start with the identity proved in part (a): cosh2(x) − sinh2(x) = 1. if we divide both sides by cosh2(x), we get 1 − sinh2(x) cosh2(x) = 1 or 1 − tanh 2(x) = .