Use the table to help answer the depreciation problems below.

a 1 2 3 4 5 6 7 8

0.6a 0.6 0.36 0.216 0.1296 0.07776 0.046656 0.0279936 0.01679616

0.7a 0.7 0.49 0.343 0.2401 0.16807 0.117649 0.0823543 0.05764801

0.8a 0.8 0.64 0.512 0.4096 0.32768 0.262144 0.2097152 0.16777216

0.9a 0.9 0.81 0.729 0.6561 0.59049 0.531441 0.4782969 0.43046721

(a) The ﬁnancial analyst for a large construction ﬁrm estimates that its heavy equipment loses 20% of its value each year. The current value can be modeled by the function V (t) = V_{0 }· 0.8 ^{t },where V_{0} is the initial value, and V (t) is the value after t years.

(I)How much is a large earthmover worth after 4 years if it cost $100,000 new?

(ii). How many years does it take for the same earthmover's value to drop below $35,000?

(b) Ofﬁce photocopiers generally get heavy use and depreciate quickly. If a copier loses 40% of its value each year, the current value can be modeled by the function V (t) = V_{0} · 0.6^{t}, where V_{0} is the initial value, and V (t) is the value after t years.

(I). If a copier costs $10,000 new, how much is it worth after 3 years? After 3 years it is worth $2,160.

(ii) How many years does it take for the same copier's value to drop below $500?

(c) A dentist estimates that her dental equipment loses 30% of its value each year.

(I). Determine the value of an x-ray machine after 4 years if it costs $200,000 new.

(ii). Determine how many years it takes for the same x-ray machine to be worth less than $20,000

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#### Top Answer

(a) (i) $ 40,960 (ii) 5 years (b)... View the full answer