Cost is expressed by the formula \(tb^4.\) If \(b\) is doubled and \(t\) remains the same, the new cost is how many time

[VJesus12]

Cost is expressed by the formula \(tb^4.\) If \(b\) is doubled and \(t\) remains the same, the new cost is how many times greater than the original cost?

(A) 1.2
(B) 2
(C) 6
(D) 8
(E) 16

[spoiler]OA=E[/spoiler]

Source: Manhattan GMAT

[orthodoxparadox]

Let \(t'\) and \(b'\) be the new parameters.

So,

\(t'\ =\ t\) and \(b'\ =\ 2\ \cdot\ b\)

New cost = \(t'\ \cdot\ b'^4\ =\ t\cdot\left(2\cdot b\right)^4\ =\ t\cdot16\cdot b^4\ =\ 16tb^4\)

So, the answer is 16 E