. Eight systems of different differential equations and four direction fields are given below. Determine the system that corresponds to each direction field and state briefly how you know your choice is correct. You should do this exercise without using technology. da (i) dt dx = x - 1 dt de = (iii) de = 2x dt = -x (ii) a + 2y (iv) dt dy = y – 1 dt dy dy dy dt dt dt da (v) da = x - 1 dt dx 22 - dx = x - 2y dt (vi) (vii) = x? – 1 (viii) dt dt dy = 2y dt dy = -y dt dy = -y dt dy = -y dt (а) (b) (c) (d) y 1114 11109 111 111

please show all steps

x = t°x1 + 2x2 + sec(t), x, = sin(t) x1 + tx2 – 3. %3D This system of linear differential equations can be put in the form x = P(t)x + g(t). Determine P(t) and g(t). help (formulas) help (matrices) P(t) : help (formulas) help (matrices) g(t):

After 25 years, your savings account has now grown to $16,200 and has an interest of 6.1% that compounds continuously. How much did you deposit at the beginning of the account