laptop computer is purchased for $$ \$ 1400 $$. After each year, the resale value decreases by $$ 35 \% $$. What will the resale value be after 4 years? Use the calculator provided and round your answer to the nearest dollar.

Question

UpStudy AI · Accepted Answer

To find the resale value of the laptop computer after 4 years, we can use the formula for exponential decay:

$$ V = P \times (1 - r)^n $$

where:
- $$ V $$ is the resale value after $$ n $$ years,
- $$ P $$ is the initial purchase price,
- $$ r $$ is the rate of decrease per year,
- $$ n $$ is the number of years.

Given:
- Initial purchase price, $$ P = \$1400 $$,
- Rate of decrease per year, $$ r = 35\% = 0.35 $$,
- Number of years, $$ n = 4 $$.

Substitute the values into the formula:

$$ V = 1400 \times (1 - 0.35)^4 $$

Now, we can calculate the resale value after 4 years using the calculator provided.
Calculate the value by following steps:
- step0: Calculate:
  $$1400\left(1-0.35\right)^{4}$$
- step1: Subtract the numbers:
  $$1400\times 0.65^{4}$$
- step2: Convert the expressions:
  $$1400\left(\frac{13}{20}\right)^{4}$$
- step3: Simplify:
  $$1400\times \frac{13^{4}}{20^{4}}$$
- step4: Evaluate the power:
  $$1400\times \frac{28561}{20^{4}}$$
- step5: Rewrite the expression:
  $$20\times 70\times \frac{28561}{20^{4}}$$
- step6: Reduce the numbers:
  $$70\times \frac{28561}{20^{3}}$$
- step7: Rewrite the expression:
  $$10\times 7\times \frac{28561}{20^{3}}$$
- step8: Rewrite the expression:
  $$10\times 7\times \frac{28561}{10^{3}\times 2^{3}}$$
- step9: Reduce the numbers:
  $$7\times \frac{28561}{10^{2}\times 2^{3}}$$
- step10: Multiply:
  $$\frac{7\times 28561}{800}$$
- step11: Multiply:
  $$\frac{199927}{800}$$
The resale value of the laptop computer after 4 years will be approximately $249.91.
The resale value of the laptop after 4 years is approximately \$250.

laptop computer is purchased for \( \$ 1400 \). After each year, the resale value decreases by \( 35 \% \). What will the resale value be after 4 years? Use the calculator provided and round your answer to the nearest dollar.

Solución de inteligencia artificial de Upstudy

Responder

Solución

Bonus Knowledge

preguntas relacionadas

Latest Arithmetic Questions