Math / Algebra

QuestionAntall passasjerer med KLM som flyr Business-class er på ca 20000 persont i året. Dette antallet har avtatt med $12 \%$ for hvert år de siste årene. Vi antar at dette antallet vil fortsette å synke med $12 \%$ i året hvert år fremover. a. Hvor mange vil reise på Business Class om fire år? Avrund til nærmeste heltall. b. Hvor mange reiste på KLM Business Class for fem år siden? Avrund til nærmeste heltall.

Studdy Solution

STEP 1

What is this asking? If 20,000 people fly KLM Business-class each year, and that number decreases by 12% yearly, how many will fly in 4 years, and how many flew 5 years ago? Watch out! Don't forget that a 12% decrease means we keep 88% (100% - 12% = 88%) each year!
Also, don't mix up calculations for the future and the past – they use different approaches!

STEP 2

1. Calculate Future Passengers
2. Calculate Past Passengers

STEP 3

Alright, future business-class travelers, let's calculate!
We start with our initial value of $20,000$ passengers.

STEP 4

Since the number decreases by $12\%$ each year, we multiply by $1 - 0.12 = 0.88$ to find the number of passengers after each year.
This $0.88$ is our magic multiplier!

STEP 5

To find the number of passengers in four years, we apply our magic multiplier four times: $20,000 \cdot 0.88 \cdot 0.88 \cdot 0.88 \cdot 0.88$ .
This is the same as $20,000 \cdot (0.88)^4$ .
Think of it like compounding, but for decreasing numbers!

STEP 6

Crunching the numbers: $20,000 \cdot (0.88)^4 \approx 20,000 \cdot 0.60 \approx 12,000$ .
So, in four years, approximately 12,000 passengers will be flying KLM Business-class.

STEP 7

Now, let's rewind and see how many passengers were flying five years ago.
Again, we start with our current $20,000$ passengers.

STEP 8

This time, we're going back in time, so we need to reverse the decrease.
Instead of multiplying by $0.88$ , we divide by $0.88$ for each year.
This is like "undoing" the decrease!

STEP 9

To find the number of passengers five years ago, we divide by $0.88$ five times: $20,000 / (0.88)^5$ .

STEP 10

Calculating the result: $20,000 / (0.88)^5 \approx 20,000 / 0.53 \approx 37,736$ .
Rounding to the nearest whole number, we get 37,736 passengers flying KLM Business-class five years ago.

STEP 11

In four years, approximately 12,000 passengers will be flying KLM Business-class.
Five years ago, approximately 37,736 passengers were flying KLM Business-class.

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Studdy Solution

STEP 1

STEP 2

1. Calculate Future Passengers
2. Calculate Past Passengers

STEP 3

Alright, future business-class travelers, let's calculate!
We start with our initial value of $20,000$ passengers.

STEP 4

Since the number decreases by $12\%$ each year, we multiply by $1 - 0.12 = 0.88$ to find the number of passengers after each year.
This $0.88$ is our magic multiplier!

STEP 5

To find the number of passengers in four years, we apply our magic multiplier four times: $20,000 \cdot 0.88 \cdot 0.88 \cdot 0.88 \cdot 0.88$ .
This is the same as $20,000 \cdot (0.88)^4$ .
Think of it like compounding, but for decreasing numbers!

STEP 6

Crunching the numbers: $20,000 \cdot (0.88)^4 \approx 20,000 \cdot 0.60 \approx 12,000$ .
So, in four years, approximately 12,000 passengers will be flying KLM Business-class.

STEP 7

Now, let's rewind and see how many passengers were flying five years ago.
Again, we start with our current $20,000$ passengers.

STEP 8

This time, we're going back in time, so we need to reverse the decrease.
Instead of multiplying by $0.88$ , we divide by $0.88$ for each year.
This is like "undoing" the decrease!

STEP 9

To find the number of passengers five years ago, we divide by $0.88$ five times: $20,000 / (0.88)^5$ .

STEP 10

Calculating the result: $20,000 / (0.88)^5 \approx 20,000 / 0.53 \approx 37,736$ .
Rounding to the nearest whole number, we get 37,736 passengers flying KLM Business-class five years ago.

STEP 11

In four years, approximately 12,000 passengers will be flying KLM Business-class.
Five years ago, approximately 37,736 passengers were flying KLM Business-class.

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Studdy Solution

STEP 1

STEP 2

1. Calculate Future Passengers2. Calculate Past Passengers

STEP 3

Alright, future business-class travelers, let's calculate!We start with our **initial value** of 20,00020,00020,000 passengers.

STEP 4

Since the number decreases by 12%12\%12% each year, we **multiply** by 1−0.12=0.881 - 0.12 = 0.881−0.12=0.88 to find the number of passengers after each year.This 0.880.880.88 is our **magic multiplier**!

STEP 5

STEP 6

**Crunching the numbers**: 20,000⋅(0.88)4≈20,000⋅0.60≈12,00020,000 \cdot (0.88)^4 \approx 20,000 \cdot 0.60 \approx 12,00020,000⋅(0.88)4≈20,000⋅0.60≈12,000.So, in four years, approximately **12,000** passengers will be flying KLM Business-class.

STEP 7

Now, let's rewind and see how many passengers were flying five years ago.Again, we start with our **current** 20,00020,00020,000 passengers.

STEP 8

This time, we're going *back* in time, so we need to *reverse* the decrease.Instead of multiplying by 0.880.880.88, we **divide** by 0.880.880.88 for each year.This is like "undoing" the decrease!

STEP 9

To find the number of passengers five years ago, we divide by 0.880.880.88 five times: 20,000/(0.88)520,000 / (0.88)^520,000/(0.88)5.

STEP 10

**Calculating the result**: 20,000/(0.88)5≈20,000/0.53≈37,73620,000 / (0.88)^5 \approx 20,000 / 0.53 \approx 37,73620,000/(0.88)5≈20,000/0.53≈37,736.Rounding to the nearest whole number, we get **37,736** passengers flying KLM Business-class five years ago.

STEP 11

In four years, approximately **12,000** passengers will be flying KLM Business-class.Five years ago, approximately **37,736** passengers were flying KLM Business-class.

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Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

1. Calculate Future Passengers
2. Calculate Past Passengers

Alright, future business-class travelers, let's calculate!
We start with our initial value of $20,000$ passengers.

Since the number decreases by $12\%$ each year, we multiply by $1 - 0.12 = 0.88$ to find the number of passengers after each year.
This $0.88$ is our magic multiplier!

Crunching the numbers: $20,000 \cdot (0.88)^4 \approx 20,000 \cdot 0.60 \approx 12,000$ .
So, in four years, approximately 12,000 passengers will be flying KLM Business-class.

Now, let's rewind and see how many passengers were flying five years ago.
Again, we start with our current $20,000$ passengers.

This time, we're going back in time, so we need to reverse the decrease.
Instead of multiplying by $0.88$ , we divide by $0.88$ for each year.
This is like "undoing" the decrease!

To find the number of passengers five years ago, we divide by $0.88$ five times: $20,000 / (0.88)^5$ .

Calculating the result: $20,000 / (0.88)^5 \approx 20,000 / 0.53 \approx 37,736$ .
Rounding to the nearest whole number, we get 37,736 passengers flying KLM Business-class five years ago.

In four years, approximately 12,000 passengers will be flying KLM Business-class.
Five years ago, approximately 37,736 passengers were flying KLM Business-class.