Answer:
She chose Option 2 which is a linear option, because it offers a smaller lose
in value compared to option 1 which is an exponential option.
The final value for option 2=$32,800
Step-by-step explanation:
Option 1
New Zoomba for 60000 with a depreciation rat of 2%per month for 3 years
Exponential equation;
y=a(1-r)^t
where;
y=future value
a=initial value=60000
r=depreciation rate=2% per month
t=time interval=12×3=36 months
Replacing;
y=60000(1-2/100)^36
y=60000(0.98)^36=28,992.79
The value after 3 years=$28,992.79
Initial value-Final value=(60000-28992.79)=$31007.21
Percentage of initial value lost=((Final value-Initial Value)/(Initial Value))×100
(31007.21/60000)×100=51.68%
Option 2
New starfish for $40,000 with a depreciation of $200 per month for 3 years
Linear equation;
y=a-bt
where;
y=Future value
a=Initial value=$40,000
b=the depreciation amount per time interval=$200 per month for 3 years
t=time interval=(3×12)=36 months
Replacing;
y=40000-(200×36)
y=32,800
Final value=y=$32,800
Initial value-Final value=(40000-32800)=$7200
Percentage of initial value lost=((Final value-Initial Value)/(Initial Value))×100
(7200/40000)×100=18%
Option 1(51.68%)>Option 2(18%) therefor Option 1 loses value at a faster rate than Option 2
She chose Option 2 which is a linear option, because it offers a smaller lose
in value compared to option 1 which is an exponential option
