Question

5b
score: 25.63/30 answered: 12/13
progres
question 2
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tom started an entertainment company. the net value, v, of the company (in thousands of dollars) t
months after its creation is modeled by: v(t)=4t² - 24t - 28
identify the variables.
x: months and y: value (thousands of dollars)
what is the y - intercept in context? (0, - 28)
which means toms company has cost $28,000 to start up.
what was the lowest net value for toms company? - 63

Explanation:

Step1: Encontrar el vértice de la parábola

La ecuación de la parábola es \(v(t) = 4t^{2}-24t - 28\), donde \(a = 4\), \(b=-24\), \(c = - 28\).
El tiempo \(t\) en el vértice se calcula con la fórmula \(t=-\frac{b}{2a}\).
Sustituyendo los valores: \(t =-\frac{-24}{2\times4}=\frac{24}{8} = 3\).

Step2: Calcular el valor mínimo

Sustituir \(t = 3\) en la ecuación \(v(t)\):
\(v(3)=4\times(3)^{2}-24\times3 - 28\)
\(v(3)=4\times9-72 - 28\)
\(v(3)=36-72 - 28\)
\(v(3)=-64\)

Answer:

\(-64\)