Math Problem of the Week - Algebra and Up - May 23, 2021 to May 29, 2021

Algebra and Up: 

Question: The profit earned by a coffee 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 2012. What month does the coffee company earn the least amount of money? How much do they earn?

Answer:   The coffee company earned $0 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 = 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, they earned $0 in April.