A barrel is a unit of volume measurement for oil. 1 barrel = 158.987 liters In 2023, an average of 1.794 million barrels of oil was produced on the Norwegian continental shelf each day. a) Approximately how many liters of oil were produced on the Norwegian continental shelf in 2023? Write the answer in standard form. In 2022, an average of 1.685 million barrels was produced each day. b) By what percentage did the production amount increase from 2022 to 2023?

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Five years ago, Gaute deposited his savings into an account with a fixed interest rate of 3.25% per year. Today, there is a little over 105,607 kroner in the account. a) How much will be in the account in five years? b) How much did Gaute deposit into the account five years ago?

### Oil Production on the Norwegian Continental Shelf

#### Part (a): Volume of oil produced in 2023

We are given:
- **1 barrel** = 158.987 liters
- **1.794 million barrels** of oil produced per day in 2023
- The number of days in a year = 365

To find the total volume of oil produced in 2023 in liters:
1. Convert 1.794 million barrels to barrels:  
   \( 1.794 \times 10^6 \) barrels/day
2. Multiply by the number of days in the year:  
   \( 1.794 \times 10^6 \times 365 \) barrels/year
3. Multiply by 158.987 liters per barrel to convert to liters:  
   \( (1.794 \times 10^6 \times 365) \times 158.987 \) liters

Let's calculate this.

\[
1.794 \times 10^6 \times 365 \times 158.987 \approx 1.0403 \times 10^{11} \text{ liters}
\]

So, approximately **\( 1.0403 \times 10^{11} \) liters** of oil were produced on the Norwegian continental shelf in 2023.

#### Part (b): Percentage increase in production from 2022 to 2023

We are given:
- 2022 daily production = 1.685 million barrels
- 2023 daily production = 1.794 million barrels

To calculate the percentage increase:
1. Calculate the increase in production:
   \[
   1.794 - 1.685 = 0.109 \text{ million barrels}
   \]
2. Use the percentage increase formula:
   \[
   \text{Percentage increase} = \left( \frac{0.109}{1.685} \right) \times 100
   \]

Let's calculate this:

\[
\frac{0.109}{1.685} \times 100 \approx 6.47\%
\]

So, the production increased by approximately **6.47%** from 2022 to 2023.

---

### Gaute's Savings Account

#### Part (a): Future value of the account in five years

We are given:
- Current amount: 105,607 kroner
- Interest rate: 3.25% per year
- We want to find the amount in the account in 5 years.

The formula for compound interest is:
\[
A = P(1 + r)^t
\]
Where:
- \(A\) = the amount in the account after \(t\) years
- \(P\) = the principal (initial deposit)
- \(r\) = annual interest rate (as a decimal)
- \(t\) = time in years

First, we calculate the future value, starting with the current amount of 105,607 kroner:
\[
A = 105,607(1 + 0.0325)^5
\]

Let's calculate this:

\[
A \approx 105,607 \times 1.0325^5 \approx 124,434 \text{ kroner}
\]

So, after 5 years, Gaute will have approximately **124,434 kroner** in the account.

#### Part (b): Initial deposit five years ago

To find the initial deposit \(P\), we use the same compound interest formula, but we solve for \(P\):
\[
P = \frac{A}{(1 + r)^t}
\]
Where:
- \(A = 105,607\) kroner (the current balance)
- \(r = 0.0325\)
- \(t = 5\)

Let's calculate this:

\[
P = \frac{105,607}{1.0325^5} \approx \frac{105,607}{1.1732} \approx 90,004 \text{ kroner}
\]

So, Gaute deposited approximately **90,004 kroner** five years ago.

---

### Questions for Exploration:
1. How many barrels of oil were produced on average each month in 2023?
2. If the interest rate was 4%, how much more would Gaute have in 5 years compared to 3.25%?
3. What is the total amount of interest Gaute earned in the past 5 years?
4. How does the percentage increase in oil production compare to historical trends over the last decade?
5. What would be the production increase in liters from 2022 to 2023?

### Tip: 
When calculating compound interest, remember that small changes in the interest rate can lead to significant differences over time, especially with longer periods!

A barrel is a unit of volume measurement for oil. 1 barrel = 158.987 liters. In 2023, an average of 1.794 million barrels of oil was produced on the Norwegian continental shelf each day. a) Approximately how many liters of oil were produced on the Norwegian continental shelf in 2023? Write the answer in standard form. In 2022, an average of 1.685 million barrels was produced each day. b) By what percentage did the production amount increase from 2022 to 2023? 

Five years ago, Gaute deposited his savings into an account with a fixed interest rate of 3.25% per year. Today, there is a little over 105,607 kroner in the account. a) How much will be in the account in five years? b) How much did Gaute deposit into the account five years ago?

Solve problems involving oil production and compound interest. Learn how to convert barrels to liters, calculate percentage increases in oil production between 2022 and 2023, and compute future and initial savings using compound interest formulas. Suitable for Grades 10-12.

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