Linearfunktion aufstellen - Lösungsweg

Question

Aufgabe:

Suppose that the value V of a machine (in EUR) is given by the following function which depends on the age t of the machine (in years):
V(t) = 2400·(30−2t)/t+3      t≥0 

d) Determine a linear function V (t) with original value and service life as in part a) and part b). In this case, how many years does it take for the machine to lose 60% of its original value

Problem/Ansatz:

Lösung habe ich bereits gegeben, jedoch keine Ahnung wie man darauf kommt:

d) V (t) = −1600 t+24000, and it takes 9 years for the machine to lose 60% of its original

Answer 1

Du suchst eine lineare Funktion, welche dieselben Achsenabschnitte hat.

f(t) = 2400·(30 - 2·t)/(t + 3)

f(0) = 24000

f(t) = 2400·(30 - 2·t)/(t + 3) = 0 --> t = 15

V(t) = 24000 - 24000/15·t = 24000 - 1600·t

V(t) = 24000 - 1600·t = 24000·(1 - 0.6) --> t = 9 Jahre