The value of cement mixer after t year is [tex]f(t) = 54,205(0. 87)^{t}[/tex]
Given to us
The value of cement mixer when bought, [tex]P[/tex]= $ 54,205
the value of cement mixer after 1 year, [tex]P_1[/tex]= $ 47,158. 35
the value of cement mixer after 2 year,[tex]P_2[/tex]= $ 41,027. 76
To find out depreciation we can use the formula for depreciation,
[tex]P_n= P(1-r)^n\\where,\\P_n= Value\ of\ asset\ after\ n\ year\\P= Value\ of\ asset\ when\ bought\\r= rate\ of\ depreciation\\n= number\ of\ years[/tex]
By putting the value, in the formula we get,
[tex]P_1= P(1-r)^n\\\\47,158.35= 54,205\times (1-r)^1\\\\\dfrac{47,158.35}{54,205} = (1-r)\\\\0.87=1-r\\\\r=0.13[/tex]
Therefore, putting the value of [tex]r[/tex] and [tex]P[/tex] in depreciation formula for [tex]t[/tex] years we get,
[tex]P_n= P(1-r)^n[/tex]
[tex]f(t) = 54,205(0. 87)^{t}[/tex]
Hence, the value of cement mixer after t year is [tex]f(t) = 54,205(0. 87)^{t}[/tex].
To know more visit:
https://brainly.com/question/3023490
