The following function represents the value of a house after x years: f(x) = 242,000(0.96)x What does 0.96 represent?

Mathematics

1 answer:

9966 [12]3 years ago

5 0

Because the 0.96 is less than 1, it means that the house loses value over the years.

Convert 0.96 to a percent: 0.96 = 96%

100% - 96% = 4%

The house loses 4% of it's value every year.

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By rounding to one significant figure 615 x 38

Lunna [17]

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20000

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4 years ago

Please check for me and if any are incorrect please explain!

Anika [276]

Answer: (1) 14.4% (2) 3.78% (3) $222.48 (4) 21,176.47

(5) $425 (6) 14.3 cents per mile

Step-by-step explanation:

1) This is a calculator question. I = 0.144 --> 14.4%

$A=P\bigg(1+\dfrac{r}{n}\bigg)^{nt}\\\\\bullet \text{A = Accrued amount (total amount paid)}\\\bullet \text{P = Principal (initial cost of the car)}\\\bullet \text{r = rate (interest rate in decimal form)}\\\bullet \text{n = number of times in a year (number of months)}\\\bullet \text{t = number of years}\\\\A = m \times nt\\\bullet \text{m = monthly payment amount}\\\bullet \text{nt = number of payments made}\\\implies m\times nt=P\bigg(1+\dfrac{r}{n}\bigg)^{nt}$

2) m = 93.33

nt = 36

P = 3000

n = 12

$m\times nt=P\bigg(1+\dfrac{r}{n}\bigg)^{nt}\\\\\\93.33\times 36=3000\bigg(1+\dfrac{r}{12}\bigg)^{36}\\\\\\3359.88=3000\bigg(1+\dfrac{r}{12}\bigg)^{36}\\\\\\1.11996=\bigg(1+\dfrac{r}{12}\bigg)^{36}\\\\\\1.00315198=1+\dfrac{r}{12}\\\\\\0.00315198=\dfrac{r}{12}\\\\\\0.0378=r\\\\\\\large\boxed{3.78\%}=r$

3) same equation as #2 but deduct the down payment from the Principal

nt = 42

P - d = 5,555 - 555 = 5,000

r = 18% --> 0.18

n = 12

$m\times nt=P\bigg(1+\dfrac{r}{n}\bigg)^{nt}\\\\\\m\times 42=(5,555-555)\bigg(1+\dfrac{.18}{12}\bigg)^{42}\\\\\\42m=5000(1.015)^{42}\\\\\\42m=5000(1.868847)\\\\\\42m=9344.23557\\\\\\m=\large\boxed{222.48}$