Math Problem of the Week - Algebra and Up - Dec. 5, 2021 to Dec. 11, 2021

Algebra and Up: 

Question: The profit earned by a cat-sitting company, measured in thousands of dollars, is modeled by the function f(t) = t² – 8t + 16, wherein t is measured in months and t = 1 is January. During which month does the cat-sitting company earn the least amount of money? How much do they earn?

Answer:  They earned $0.00 in April.

Solution:  This function is a parabola that opens upward, so the lowest value is at the vertex. To find the month, we find ^–b/_2a = ^–(–8)/_{(2 × 1)} = ⁸/₂ = 4. So the vertex is at t = 4, which represents the month of April. To find how much they earned, we set t = 4 and solve: 4² – 8(4) + 16 = 16 – 32 + 16 = 0. So, the cat-sitting business earned $0.00 in April.