Matematik 1. FÖRÄNDRINGSFAKTOR OCH UPPREPAD PROCENTUELL FÖRÄNDRING

Summary

The video script explains the concept of the change factor (CF) and percentage change. It illustrates how to calculate the new amount after a percentage increase or decrease using the CF method. The script also covers repeated percentage changes and exponential growth, demonstrating how to multiply CFs to find total changes over multiple periods. It concludes with calculating total percentage change when only the final value is known.

Takeaways

• 📈 The change factor (förändringsfaktor) is used to calculate the new amount after a percentage increase or decrease.
• 💹 To find the new amount after an increase, multiply the original amount by 1 plus the change factor in decimal form (e.g., a 15% increase has a change factor of 1.15).
• 📉 For a decrease, subtract the percentage decrease from 100% to find the remaining percentage, then use it as the change factor in decimal form (e.g., a 15% decrease has a change factor of 0.85).
• 🔢 The change factor is always the new value divided by the old value, which can be used to find the new value when the old value and change factor are known.
• 🔄 For repeated percentage changes, multiply the change factors together to find the total change factor.
• 🔢 Exponential change occurs when the same percentage change occurs multiple times, and it can be represented by raising the change factor to the power of the number of changes.
• 📊 When you don't know the old or new value but need to find the total percentage change, multiply the individual change factors together.
• 📐 If there are multiple changes with different percentages, you can still multiply the change factors to find the total change factor.
• 🔢 The formula for repeated percentage changes can be written as y = c * (change factor)^x, where y is the new value, c is the old value, and x is the number of changes.
• 📉 If something decreases by a certain percentage and then increases by the same percentage, the total change factor is the product of the change factors for decrease and increase.

Q & A

What is a change factor?

A change factor, often abbreviated as FF, represents the percentage of the original value after a change. It is calculated by dividing the new value by the old value.

How do you calculate the new amount with a change factor when an amount increases by a certain percentage?

To calculate the new amount when an amount increases by a certain percentage, you can either add the percentage of the increase to the original amount or multiply the original amount by the change factor (which is 1 plus the percentage increase in decimal form).

What is the change factor when an amount decreases by 15%?

When an amount decreases by 15%, the change factor is 0.85, which represents 85% of the original amount (100% - 15% = 85%).

How can you calculate the total change factor for a series of percentage changes?

To calculate the total change factor for a series of percentage changes, you multiply the individual change factors together.

What is an exponential change?

An exponential change is a situation where the same percentage change occurs repeatedly over a certain period. The change factor can be expressed as a power of the same factor.

How do you calculate the new value with a repeated percentage increase?

To calculate the new value with a repeated percentage increase, you multiply the original value by the change factor raised to the power of the number of times the change occurs.

What does the total change factor represent when you don't know the old or new value?

The total change factor represents the overall percentage change from the original value to the final value when you don't know either value. It is calculated by multiplying the change factors of each individual change.

How can you find the total percentage change when you have the total change factor?

To find the total percentage change when you have the total change factor, you subtract 1 from the change factor and then multiply by 100 to convert it to a percentage.

What happens to the value if it first decreases by 20% and then increases by 20%?

If a value first decreases by 20% and then increases by 20%, the total change factor is calculated by multiplying 0.80 (the change factor for a 20% decrease) by 1.20 (the change factor for a 20% increase), resulting in a total change factor of 0.96, which means the final value is 96% of the original, a net decrease of 4%.

Why are change factors useful for repeated percentage changes?

Change factors are useful for repeated percentage changes because they simplify the calculation process by allowing you to multiply the change factors together instead of calculating the percentage of the new value each time.