At time t=3, there are 2.5 cubic feet of water in the tub. Write an equation for the locally linear approximation of W at t=3, and use it to approximate the volume of water in the tub at time t=3.5

W=0.8333*t

2.917 ft³

Step-by-step explanation:

At time t=3, there is 2.5 ft³ of water in the tub

Finding the relation will be;

3=2.5

1=?

Rate=0.8333 ft³/min

W=0.8333 ft³ / min

W=0.8333*t

At t=3.5 will be;

1 min = 0.8333

3.5 min = ?

Apply cross-production

3.5*0.8333 = 2.917 ft³

W = 2.952 cubic feet.

Step-by-step explanation:

From the equation given, we recall that,

At time t = 3, w = 2.5

Using Linear Approximation

(W - 2.5) = w¹ (3) { t - 3} - [ W¹ (3) = f (3) = tan⁻¹ (π) / 2 - 3/10 = 0.904

W = 2.5 + 0.904 (t - 3)

W = 2.5 + 0.904t - 2.712

W = 0.904t - 0.212

at t = 3

W = 0.904 (3.5) - 0.212

W = 2.952

Therefore the cubic feet is 2.952