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) = _

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)

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) = _______

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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) = _