Question 1 1 pts Find the general solution to the equation dy at = (1 + t) (1 +y) O y(t ) = In(t + + + c) y(t ) = Cett? - 1 O y ( t ) = ett i t c O y ( t ) = t+ +cQuestion 2 1 pts Find the general solution to the equation dy = etty+3 dt O y(t) = In(t + 3 + c) O y ( t ) = t+3+c O y ( t ) = -et+3 + c O y(t) = - In(c- et+3)Question 3 1 pts Find the (specific) solution to the following initial value problem: dy 2t dt y(2) = 3 ytyt2 O y(t) = -2In(1 + t2) + 9 -In(5) O y(t) = \\2In(1 + +2) + 9 - 2In(5) O y(t) = 2In(1+ +2) + 9 -In(5) O y(t) = -2In(1+ t2 ) +9 -In(5)Question 4 1 pts A common inhabitant of human intestines is the bacterium Escherichiacoli. A cell of this bacterium in a nutrientbroth medium divides into two cells every 20 minutes, and its initial population is 30 cells. Find the number of cells after 5 hours. 0 450 0 32,768 0 24,300,000 0 983,040 Question 5 1 pts A population is modeled by the differential equation dt de _ 1.1P (1 P 5800 For what values of P is the population decreasing? OP > 5800 O0

1.1Biologists stocked a lake with 350 sh and estimated the carrying capacity to be 5250. The number of sh quadrupled in the rst year. Assuming that the size of the sh population satises the logistic equation, nd an expression for the size of the population after t years. omp Gauz OP(t)=% OP(t)=%