Respuesta :
Answer:
The answer is "$238".
Step-by-step explanation:
Current worth[tex]= \$ 17,000[/tex]
depreciates by [tex]\frac{1}{2}[/tex] in 3 years.
time= 19 years
depreciates rate=?
Using formula:
[tex]\to \text{Worth= Current worth}(1- \frac{\text{depreciates rate}}{100})^{time}[/tex]
[tex]\to A_t=A_0(1-\frac{r}{100})^t[/tex]
calculates depreciate value in 3 year [tex]= \frac{1}{2} \times 17,000[/tex]
[tex]= 8,500[/tex]
so,
[tex]A_t=8,500\\\\A_0=17,000\\\\t=3\ years[/tex]
[tex]\to A_t=A_0(1-\frac{r}{100})^t\\\\\to 8,500= 17,000(1-\frac{r}{100})^3\\\\\to \frac{8,500}{17,000}= (1-\frac{r}{100})^3\\\\\to \frac{1}{2}= (1-\frac{r}{100})^3\\\\\to (\frac{1}{2})^{\frac{1}{3}}= (1-\frac{r}{100})\\\\\to 0.793700526 = (1-\frac{r}{100})\\\\\to \frac{r}{100} = (1-0.793700526)\\\\\to \frac{r}{100} = (1-0.8)\\\\\to r= 0.2 \times 100 \\\\\to r= 20 \%[/tex]
depreciates rate= 20%
[tex]\to \text{Worth= Current worth}(1- \frac{\text{depreciates rate}}{100})^{time}[/tex]
[tex]= \$ 17,000 (1- \frac{20}{100})^{19}\\\\= \$ 17,000 (1-0.2)^{19}\\\\= \$ 17,000 (0.8)^{19}\\\\= \$ 17,000 \times 0.014\\\\= \$ 238[/tex]
Answer:
200
Step-by-step explanation:
Halving Formula:
y=a\left(\frac{1}{2}\right)^{\frac{t}{h}}
y=a(
2
1
)
h
t
a=17000\hspace{40px}h=3\hspace{40px}t=19
a=17000h=3t=19
h is the halving time
\text{Plug in:}
Plug in:
y=17000\left(\frac{1}{2}\right)^{\frac{19}{3}}
y=17000(
2
1
)
3
19
y=210.826702215
y=210.826702215
y\approx 200
y≈200
