The formula for depreciation is:
[tex] y=x(1-r)^t [/tex]
Where x = Initial value,
y= Amount after depreciation.
r= Rate of depreciation,
t = time (in years)
According to given problem,
x = 1040, y= 944 and t = 12 months =1 year.
So, first step is to plug in these values in the above formula, So,
[tex] 944 = 1040(1-r)^1 [/tex]
944 = 1040 (1 -r)
[tex] \frac{944}{1040} =1-r [/tex] Divide each sides by 1040.
0.907692308 =1 - r
0.907692308 - 1 = -r Subtract 1 from each sides.
-0.092307692 = -r
So, r = 0.09 or 9%.
Now plug in 0.09 in the above equation to get the depreciation equation. So,
[tex] y = x (1- 0.09)^t [/tex]
So, [tex] y = 0.91x^t [/tex]
b) To find the value of the bike after 5 months,
plug in t = 5 months= 5/12 = 0.41667 years in the above equation of depreciation.
So, [tex] y= 1040 *(0.91)^{0.41667} [/tex]
y = 1040 * 0.961465659
y = 999.9242852
y = 1000 (Rounded to nearest integer).
Hence, the value of the bike after 5 months is $1000.
