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.
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