I think it is C. but I am not sure so please help me if you can

Question

A machine is set up to cut metal strips of varying lengths and widths based on the time  in minutes. The change in length is given by the function , and the change in width is given by . Which function gives the change in area of the metal strips?

A. 

B. 

C. 

D. 

Answer 1

First of all √t = t^1/2

Don't let yourself get thrown by alternative notations.

Second, A = lw is still true.

So we have A = lw, which here is l(t) • w(t).

This gives us A(t) = (t² - t^1/2) • (t²- 2t^1/2)

FOIL gives us t⁴ - 3t^5/2 + 2t

Choice C is correct.

Answer 2

Since the question provides expressions for length and width, we can write an expression for area in the following way,

Area = (Length)(Width)

A(t) = l(t)w(t)

Now, we can plug in our expressions for length, l(t), and width, w(t), then multiply.

A(t) = (t² - t^1/2)(t² - 2t^1/2)

A(t) = t⁴ - t^5/2 - 2t^5/2 + 2t [using the FOIL method]

A(t) = t⁴ - 3t^5/2 + 2t [combine like terms]

Therefore, the area can be expressed as A(t) = t⁴ - 3t^5/2 + 2t, which is answer C.