Problem 58 - Elementary Algebra

Question

In the second quarter of 2006 , the revenue of a biotechnology company that sells cancer drugs was \(\$ 2.2\) billion. In the second quarter of 2007 , its revenue was \(\$ 3\) billion. Find the percent increase in revenue. Round to the nearest percent. (Source: www.nytimes.com, July 12,2007 )

Step-by-Step Solution

Answer

The percent increase in revenue is approximately 36%.

Step 1: Identify Initial and Final Values

The initial revenue (in 2006) is \( R_{2006} = 2.2 \text{ billion dollars} \). The final revenue (in 2007) is \( R_{2007} = 3 \text{ billion dollars} \).

Step 2: Calculate Change in Revenue

Subtract the initial revenue from the final revenue to find the change in revenue: \( \text{Change in revenue} = R_{2007} - R_{2006} = 3 - 2.2 = 0.8 \text{ billion dollars} \).

Step 3: Calculate Percent Increase

Use the percent increase formula: \[ \text{Percent Increase} = \frac{\text{Change in Revenue}}{\text{Initial Revenue}} \times 100 \]. Substituting the values: \[ \text{Percent Increase} = \frac{0.8}{2.2} \times 100 \approx 36.36 \% \].

Step 4: Round to the Nearest Percent

Round 36.36% to the nearest whole number, which gives \(\text{Percent Increase} \approx 36 \% \).

Key Concepts

percent increase

Understanding percent increase is crucial for comparing how much a quantity grows over time. It shows the change in the form of a percentage, making it easier to grasp.

For example, if the revenue of a company grows from 2.2 billion dollars to 3 billion dollars in one year, the percent increase tells us how much larger the second number is compared to the first.

The formula to calculate the percent increase is: \[ \text{Percent Increase} = \frac{\text{Change in Revenue}}{\text{Initial Revenue}} \times 100 \]

This formula takes the change in value, divides it by the original value, and multiplies by 100 to convert it into a percentage. It's a straightforward way to understand numerical growth.

revenue change

Revenue change is the difference between the revenue at two different times.

To find the change in revenue:

• Subtract the initial revenue from the final revenue.

In our example, the company's revenue in 2006 was 2.2 billion dollars, and in 2007, it was 3 billion dollars.

Calculating the change: \[ \text{Change in Revenue} = R_{2007} - R_{2006} = 3 - 2.2 = 0.8 \]

Therefore, the revenue increased by 0.8 billion dollars.

This increase is essential to understand the company's growth before converting it into a percentage.

elementary algebra

Elementary algebra is the backbone of finding changes and percentages. It involves basic operations like addition, subtraction, and division.

When calculating percent increase, we perform the following steps which all rely on basic algebra:

• Identify the initial and final values.
• Subtract to find the change.
• Divide the change by the initial value.
• Convert the result into a percentage.

These operations are simple but fundamental.

Grasping elementary algebra ensures you can handle similar financial calculations with ease.

step-by-step solution

A step-by-step solution breaks down complex problems into manageable parts. It helps in understanding each component and how they connect.

Here's how we solved the increase in revenue:

• Step 1: Identify the initial and final values. The initial revenue is 2.2 billion dollars, and the final is 3 billion dollars.
• Step 2: Calculate the change in revenue. Subtract the initial value from the final value: 3 - 2.2 = 0.8 billion dollars.
• Step 3: Compute the percent increase. Divide the change by the initial value and multiply by 100: \[ \frac{0.8}{2.2} \times 100 \approx 36.36\% \]
• Step 4: Round to the nearest percent. The answer is 36%.

A step-by-step approach makes the problem easier to solve and understand, ensuring you don't miss any critical steps.