Tom started an entertainment company. The net value of the company (in thousands of dollars) ttt months after its creation is mo

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Tom started an entertainment company. The net value of the company (in thousands of dollars) ttt months after its creation is mo

deled by v(t)=4t^2-24t-28v(t)=4t 2 −24t−28v, left parenthesis, t, right parenthesis, equals, 4, t, squared, minus, 24, t, minus, 28 Tom wants to know when his company will be at its lowest net value. 1) Rewrite the function in a different form (factored or vertex) where the answer appears as a number in the equation. v(t)=v(t)=v, left parenthesis, t, right parenthesis, equals 2) How many months after its creation does the company reach its lowest net value? months

Mathematics

1 answer:

zzz [12.3K] · Answer 1 · 2026-04-09T21:56:20+03:00

Step-by-step explanation: The entertainment company’s net value after t months can be expressed by the equation; v(t) = 4t² - 24t - 28. To factor this expression, we need to simplify the equation: v(t) = 4t² - 24t - 28, dividing everything by 4 yields: v(t) = t² - 6t - 7, v(t) = t² - 7t + t - 7, v(t) = t(t-7) + 1(t-7), v(t) = (t+1)(t-7). Thus, the function in factored form is v(t) = (t+1)(t-7). To find when the company hits its lowest value, substitute v(t) = 0 into the factored expression: v(t) = (t+1)(t-7). Setting equal to zero provides: (t+1)(t-7) = 0, leading to t + 1 = 0 and t - 7 = 0; thus, t = -1 and t = 7. Since time cannot be negative, therefore, t equals 7 months. This indicates that after 7 months, the company will reach its minimal net value.