3.3 Rates of Change

• To calculate a variable rate of change, you need to find the change in quantity and change in time as time approaches a specific point, known as time t.
• What is the formula for calculating speed?

  Speed = Distance / Time
• A growth rate is calculated as the percentage increase of a population or investment over time.
• What is the formula for calculating cost increase as a percentage?

  Cost Increase = (Final Cost - Initial Cost) / Initial Cost * 100%
• Acceleration is an example of a variable rate of change.
• Match the type of rate with its formula:

  Constant Rate of Change ↔️ Rate = (Change in Quantity) / (Change in Time)

  Variable Rate of Change ↔️ Rate at time t = (Change in Quantity) / (Change in Time) as time approaches t
• What does the formula for a constant rate of change calculate?

  Average rate of change
• The formula for a variable rate of change calculates the instantaneous rate of change at a specific time.
• For variable rates of change, the formula involves finding the change in quantity and change in time as the time approaches a specific point
• For variable rates of change, the formula allows you to calculate the instantaneous rate of change at a specific time.
• What is the rate of change if a car travels 150 miles in 3 hours?

  50 miles per hour
• The acceleration of a bike that increases in speed from 10 mph to 20 mph in 1 hour is 10 mph/hour.
• Match the application with its definition and formula:

  Speed ↔️ Distance traveled per unit of time; Speed = Distance / Time

  Growth Rate ↔️ Percentage increase over time; Growth Rate = (Final Value - Initial Value) / Initial Value * 100%

  Cost Increase ↔️ Change in the cost of goods; Cost Increase = (Final Cost - Initial Cost) / Initial Cost * 100%
• What is the typical independent variable in rates of change calculations?

  Time
• Rates of change can be either constant or variable.
• A constant rate of change remains the same over the entire time period.
• An example of a constant rate of change is speed, which is calculated as distance divided by time.
• What type of relationship is associated with a constant rate of change?

  Linear
• Knowing whether a rate of change is constant or variable is important for analyzing the relationship between two quantities.
• What is the formula for calculating a constant rate of change?

  Rate = (Change in Quantity) / (Change in Time)
• A car traveling 60 miles in 1 hour has a speed of 60 mph.
• What is the cost increase in percentage if the price of bread rises from $2 to $2.50?

  25%
• A population increasing from 1000 to 1200 in a year has a growth rate of 20%.
• Steps to apply rates of change to solve problems:

  1️⃣ Identify the quantities involved

  2️⃣ Determine if the rate is constant or variable

  3️⃣ Apply the appropriate formula

  4️⃣ Interpret the calculated rate of change
• What is the speed of a car that travels 150 miles in 3 hours?

  50 miles per hour
• The acceleration of a bike that increases in speed from 10 mph to20 mph in 1 hour is 10 mph/hour.
• If a population increases by 20% in a year, it means the population grew from 1000 to 1200.
• What does a growth rate of 20% mean for a population that started at 1000?

  Increased by 200