Question

For t > 30, L(t), the linear approximation to A at t = 30, is a better model for the amount of grass clippings remaining in the bin. Use L(t) to predict the time at which there will be 0.5 pound of grass clippings remaining in the bin. Show the work that leads to your answer.

Answer 1

35 days

Explanation:

We know that L(t) is the tangent to the line A(t) at t = 30

At t = 30:

A (30) ≈ 0.783 →(30, 0.783) = (t, A(t))

A¹ (30) ≈ -0.56

let -0.56 = M

For a linear function, a straight line equation applies which leads to

(y-y₁) = m (x-x₁) ...1

So for this problem we have;

A (t)-0.783 = -0.56 (t - 30)

when there is 0.5 pounds of grass, A (t) - 0.5, then using the equation (1)

(0.5 - 0.783) = -0.56 (t-30)

t = 35.054

≈ 35 days