Respuesta :
Answer:
The inequality 10,000 (0.85)^t < (1,000) can be used to represent the situation.
The solution set for the inequality is (14.168)
Answers: 0.85, 1,000, 14.168
The solution set for the inequality is (15, ∞).
What is depreciation?
The monetary value of an asset decreases over time due to use, wear and tear or obsolescence. This decrease is measured as depreciation.
What is compound interest for depreciation?
If the reduced value of the goods is compounded for fixed time then it is called compound depreciation.
Formula of compound interest for depreciation:
[tex]A = P(1-\frac{r}{100} )^{n}[/tex]
Where,
A= Final Amount
P = initial Principal
n = time in years
r = rate per annum
According to the question
New copier costs (p) = $10,000
depreciates in value every year (r) = 15%
The principal will replace the copier when it drops below 10% of its original value.
i.e Final amount should be less than [tex]$10,000 * \frac{10}{100}[/tex]
A is < $ 1000
Using compound interest formula :
[tex]A = P(1-\frac{r}{100} )^{n}[/tex]
[tex]1000 > 10000(1-\frac{15}{100} )^{n}[/tex]
[tex]0.1 > (0.85 )^{n}[/tex]
n ≈ 14.168
n = after 15years (next whole no)
Hence , The solution set for the inequality is (15, ∞).
To know more about compound interest for depreciation here:
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