Pls answer this with as much work as possible :)

Question

The quantity of a substance can be modeled by the function Q(t) that satisfies the differential equation dQ/dt = -1/70Q. One point on this function is Q(0)=280. Based on this model, use a linear approximation to the graph of Q at t=0 to estimate the quantity of the substance at t=-0.1.

Answer 1

If you solve the DE, the solution is Q(t) = 280e^(-1.7t) at t = -0.1, Q)t) = 331.9

The series for e^t = 1 + t + t²/2! = t³/3! .............. the linear portion being e^t = 1 + t

In our case 280e^(-1.7t) = 280{ 1 + (-1.7t) } = 280 - 476t

at t = -0.1, the linear solution is Q = 280 - 476(-.1) = 327.6