https://file.aiquickdraw.com/mathbot/file/17213201055917owz74jh.PNG

Let's solve each of the questions in the new image one by one.

### Question 4

Bruce's Electronics sold 487 tablets last year at $384.99 each. This year their price decreased to $337.99 and units sold increased to 635.

#### a) What is the percent change in price year-over-year?

To calculate the percent change in price:

\[
\text{Percent Change} = \left( \frac{\text{New Price} - \text{Old Price}}{\text{Old Price}} \right) \times 100
\]

Given:
- Old Price = $384.99
- New Price = $337.99

\[
\text{Percent Change} = \left( \frac{337.99 - 384.99}{384.99} \right) \times 100
\]

\[
\text{Percent Change} = \left( \frac{-47.00}{384.99} \right) \times 100
\]

\[
\text{Percent Change} \approx -12.21\%
\]

So, the percent change in price is approximately $-12.21\%$.

#### b) What is the percent change in units sold year-over-year?

To calculate the percent change in units sold:

\[
\text{Percent Change} = \left( \frac{\text{New Units Sold} - \text{Old Units Sold}}{\text{Old Units Sold}} \right) \times 100
\]

Given:
- Old Units Sold = 487
- New Units Sold = 635

\[
\text{Percent Change} = \left( \frac{635 - 487}{487} \right) \times 100
\]

\[
\text{Percent Change} = \left( \frac{148}{487} \right) \times 100
\]

\[
\text{Percent Change} \approx 30.39\%
\]

So, the percent change in units sold is approximately $30.39\%$.

#### c) What is the percent change in total revenue year-over-year?

First, calculate the total revenue for each year:

- Last year's revenue: $487 \times 384.99$
- This year's revenue: $635 \times 337.99$

\[
\text{Last Year's Revenue} = 487 \times 384.99 \approx 187,489.13
\]

\[
\text{This Year's Revenue} = 635 \times 337.99 \approx 214,426.65
\]

To calculate the percent change in total revenue:

\[
\text{Percent Change} = \left( \frac{\text{This Year's Revenue} - \text{Last Year's Revenue}}{\text{Last Year's Revenue}} \right) \times 100
\]

\[
\text{Percent Change} = \left( \frac{214,426.65 - 187,489.13}{187,489.13} \right) \times 100
\]

\[
\text{Percent Change} = \left( \frac{26,937.52}{187,489.13} \right) \times 100
\]

\[
\text{Percent Change} \approx 14.37\%
\]

So, the percent change in total revenue is approximately $14.37\%$.

### Question 5

To find the number of years it would take for $8,000 to grow to $30,000 with an annual rate of change of 8.611786%:

We use the compound interest formula:

\[
A = P \left(1 + \frac{r}{100}\right)^n
\]

Given:
- $A = 30,000$
- $P = 8,000$
- $r = 8.611786\%$
- $n$ is the number of years

Rearranging the formula to solve for $n$:

\[
n = \frac{\log{\left(\frac{A}{P}\right)}}{\log{\left(1 + \frac{r}{100}\right)}}
\]

\[
n = \frac{\log{\left(\frac{30,000}{8,000}\right)}}{\log{\left(1 + \frac{8.611786}{100}\right)}}
\]

\[
n = \frac{\log{3.75}}{\log{1.08611786}}
\]

\[
n \approx \frac{0.57403}{0.03604}
\]

\[
n \approx 15.93
\]

Rounding to the nearest whole year, it would take approximately $16$ years for $8,000 to grow to $30,000 at an annual rate of change of 8.611786%.

---

Would you like any details or further explanation on any of these calculations?

Here are some more questions you might find interesting:
1. How do you calculate the area under a curve using integration?
2. What is the formula for calculating compound interest continuously?
3. How do you solve quadratic inequalities?
4. What is the significance of eigenvalues and eigenvectors in linear algebra?
5. How do you find the standard deviation of a set of data?

**Tip:** When working with percentages, always remember to convert percentage rates to their decimal form before using them in calculations.

Explore how to calculate percent change and compound interest with detailed step-by-step solutions. This problem involves computing the percent change in price, units sold, and total revenue, along with determining the time required for an investment to grow using compound interest. Suitable for advanced high school students and beyond.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation