An operations manager observes a new production process. Based on production of the first 32 units, the manager estimates that the learning rate is 85%. If unit #32 took 23.52 minutes to complete and the manger is correct about the learning rate, how long will unit #128 take to complete?

The answer is 17.01 minutes

Explanation:

Given that:

The learning rate (r) = 85% = 0.85

T₃₂= 23.52 minutes

By applying the learning curve formula

Thus,

Tₙ = T₁ nᵇ

Where b represent ln(r)/ln2

b = ln( 0.85)/ln2 = -0.2344

23.55 = T₁ * (32)^-0.2344

T₁ = 23.55 * (32)^0.2344

Now,

T₁₂₈ = T₁ (128)^ - 0.2344

= 23.55 * (32)^0.2344 * (128)^ - 0.2344

=17.01 minutes

among other factors, composers started writing dynamic markings in their scores because "new instruments allowed for more dynamic ranges and contrast."

dynamics allude to the loudness or softness of music. dynamics offer an approach to demonstrate articulation in sheet music. they to drive the enthusiastic substance of music through volume and force. maybe you could alter both the volume and the shading profundity on your screen at the same time. we can likewise think about the force side of elements as the quality of a note. a few notes are intended to be played delicately and gently, while others are intended to be played all the more firmly.  

some dynamics markings have a letter 'm,' which remains for mezzo, signifying 'medium.' so a mezzo piano unique stamping resembles this (mp) and intends to play medium calm, while a mezzo specialty dynamic resembles this (mf) and intends to play medium loud.