Question

Tom started an entertainment company. The net value of the company (in thousands of dollars)
t
tt months after its creation is modeled by
v
(
t
)
=
4
t
2
−
24
t
−
28
v(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

Answer 1

SOLUTION

TO DETERMINE

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

$\sf{v(t) = 4 {t}^{2} - 24t - 28}$

EVALUATION

Here the given that

$\sf{v(t) = 4 {t}^{2} - 24t - 28}$

1) The above equation can be rewritten as below

$\sf{v(t) = 4 {t}^{2} - 24t - 28}$

$\sf{ \implies \: v(t) = 4( {t}^{2} - 6t) -28}$

$\sf{ \implies \: v(t) = 4( {t}^{2} - 2.t.3 + {3}^{2} - {3}^{2} ) -28}$

$\sf{ \implies \: v(t) = 4 {(t - 3)}^{2} - 36 -28}$

$\sf{ \implies \: v(t) = 4 {(t - 3)}^{2} - 64}$

Which is of the vertex form

2) The rewritten form of v(t) is

$\sf{v(t) = 4 {(t - 3)}^{2} - 64}$

Now (t - 3)² is always non-negative

∴ 4(t - 3)² is always non-negative

So lowest value of 4(t - 3)² is 0 which occurs when t = 3

Consequently lowest value of v(t)

= 0 - 64

= - 64

Since lowest value of v(t) occurs when t = 3

Hence after 3 months the company reaches its lowest net value

━━━━━━━━━━━━━━━━

Learn more from Brainly :-

1. 1) Form a quadratic equation such that one of its roots is 5. Forma quadratic equation for it and write. (For the format...

https://brainly.in/question/38226428

2. Generally, what is the range of coefficient of skewness for data where the mode is ill-defined?(A) 0 to 1 (B) -1 to +1

https://brainly.in/question/26142979