Can someone help me understand these?

1.

The previous question showed how to setup an initial value problem, such as (13: a: _ = 1 _ . dt 00 100 with the initial condition that a: = 4000 when t = 0 . Now we can solve this equation for at. This differential equation is (select all that are true) linear separable C] unsolvable. Hence, we compute that a: = [1-]. E. An unidentified virus infects a small town. Each month 40 new cases are reported, and through recovery or death 6% of the infected population no longer have the disease. Let V be the number of people at time t who have the virus. Then dV 6 Initially, nobody has the disease. The solution to this initial value problem is: Va) = a. 3. Hence we can predict (to the nearest integer) the number of infected people after . 2 months: V(2) = ii 3 . 10 months: V(10) = ii 3 . 100 months: V(100) = ii 3. [31,. LA. As time goes on, we expect that the number of infected people tends to - -I-- v The effectiveness of a police force may be measured by its clearance rate: the number of charges laid in a month divided by the total number of unsolved crimes. In Arachnid Boy's home town, new crimes are reported roughly 20 times per month, and while Arachnid boy is in town, the police clearance rate is 60%. Arachnid Boy comes back from his holiday and nds there are 200 unsolved crimes. Let a: be the number of unsolved crimes at the start of month t , with t = 0 representing the rst month that Arachnid Boy is back from his holiday. We can find an equation for a: by solving the initial value problem d3: . . - dt = 20[60/100l'x o :1 crimes per month, and . initially, x = 200 o :1. The solution to this inital value problem is As time drags on, the number of unsolved crimes approaches, to the nearest integer t>oo