Question

Un servidor de internet tiene 10 años de uso y su valor actual es de $23,000.00, pero hace cuatro años su valor era de $41,400.00. Si el valor del servidor se deprecia linealmente con el tiempo, determina: La ecuación particular que relaciona el valor del servidor v con el tiempo transcurrido t. U.= t + El valor del servidor cuando era nuevo fue de: $ el valor del servidor después de 12 años de uso será de $​

Answer 1

The value of the server after 12 years of use would be $12,400.

We can use the given information to determine the equation that relates the value of the server v with the time passed t. Since the value of the server depreciates linearly with time, we can use the slope-intercept form of a linear equation:

v = mt + b

where m is the slope (the rate of depreciation) and b is the y-intercept (the value of the server when it was new).

To find the slope, we can use the two given data points: (0, value when new) and (4, 41400). The change in value over 4 years is:

change in value = current value - value 4 years ago

= 23000 - 41400

= -18400

The rate of depreciation is the change in value divided by the time interval:

m = (change in value) / (time interval)

= -18400 / 4

= -4600

Therefore, the equation that relates the value of the server v with the time passed t is:

v = -4600t + b

To find the value of b, we can use the fact that the current value of the server is $23,000 when t = 10 (since the server has been used for 10 years). Substituting these values into the equation, we get:

23000 = -4600(10) + b

b = 68000

Therefore, the equation that relates the value of the server v with the time passed t is:

v = -4600t + 68000

The value of the server when it was new would be $68,000.

To find the value of the server after 12 years of use, we can substitute t = 12 into the equation:

v = -4600(12) + 68000

v = 12400

Therefore, the value of the server after 12 years of use would be $12,400.