MathDB
Maximizing function

Source: 2020 AMC 12B #22

February 6, 2020
2020 AMCAMCalgebra2020 AMC 12BAMC 12AMC 12 B

Problem Statement

What is the maximum value of (2t−3t)t4t\frac{(2^t-3t)t}{4^t} for real values of t?t?
<spanclass=′latex−bold′>(A)</span> 116<spanclass=′latex−bold′>(B)</span> 115<spanclass=′latex−bold′>(C)</span> 112<spanclass=′latex−bold′>(D)</span> 110<spanclass=′latex−bold′>(E)</span> 19<span class='latex-bold'>(A)</span>\ \frac{1}{16} \qquad<span class='latex-bold'>(B)</span>\ \frac{1}{15} \qquad<span class='latex-bold'>(C)</span>\ \frac{1}{12} \qquad<span class='latex-bold'>(D)</span>\ \frac{1}{10} \qquad<span class='latex-bold'>(E)</span>\ \frac{1}{9}
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