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A laptop computer loses its value each month after it is purchased. Its value as a function of time, in months,

is modelled by V (m)=3800 (0.92)^m . What is the value of the laptop after 3 months? In which month after it is

purchased does the laptop’s worth fall below $2000?

Respuesta :

UncleTom
1) V(3)=3800*(0.92)^3=2959.01 Answer: 2959.02.
2) 2000=3800*(0.92)^x;
10/19=(23/25)^x
x≈7.6978.
adioabiola

The value of the laptop after 3 months given it's value as a function of time, in months as V(m) = 3800 (0.92)^m is V(m) = $2,959.01

Given:

V(m) = 3800 (0.92)^m

where,

m = number of months after purchase = 3 months

So,

V(m) = 3800 (0.92)^m

= 3800 ( 0.93)³

= 3800 (0.778688)

= 2,959.0144

Approximately,

V(m) = $2,959.01

V(m) = 3800 (0.92)^m

2000 > 3800 (0.92)^m

2000/3800 > 0.92^m

10/19 > 0.92^m

10/19 > 23/35^m

7.6978 > m

Approximately to whole month

8 months > m

Therefore, the month after the laptop’s worth fall below $2000 is 8 months

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