Let y(t) = 13(1 − e^−6t). In this question, you will show that this function satisfies the differential equation dy/dt = 6(13 − y).

1. Calculate dy/dt by differentiating the formula for y.

dy/dt =

2. Calculate 6(13 − y) by substituting the formula for y.

6(13 − y) =

y(t) = 13[1 - e^(-6t)]

does not satisfy the differential equation,

dy/dt = 6(13 - y)

Step-by-step explanation:

Given

y(t) = 13[1 - e^(-6t)](1)

We want to show that this function satisfies the differential equation dy/dt = 6(13 - y)(2)

If (1) is a solution of (2), then after differentiating (1) with respect to t, we obtain dy/dy, and substituting the value obtain for dy/dt into (2), (2) is satisfied. Otherwise, it doesn't not satisfy (2).

Now, let us do that.

y(t) = 13[1 - e^(-6t)]

Differentiating with respect to t, we have:

dy/dt = 13×(-6)[1 - e^(-6t)]

= -6×13[1 - e^(-6t)]

But y = 13[1 - e^(-6t)]

So,

dy/dt = -6y

Therefore,

y(t) = 13[1 - e^(-6t)]

does not satisfy the differential equation,

dy/dt = 6(13 - y)

step-by-step explanation:

if you meant, "on the way from (3, 2) to (3, 14):

x does not change; y increases by 12.

ensure that you have copied down this problem correctly.   .