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?

### Part 1: Oil Production on the Norwegian Continental Shelf

#### a) **Total oil production in liters in 2023**

We are given the following data### Part 1: Oil Production on the Norwegian Continental Shelf

#### a) **Total oil production in liters in 2023**

We are given the following 
- 1 barrel = 158.987 liters
- Average oil production in 2023 = 1.794 million barrels/day = \(1.794 \times 10^6\) barrels/day
- There are 365 days in a year.

The total oil production in liters for 2023 is calculated as:
\[
\text{Total liters} = 1.794 \times 10^6 \, \text{barrels/day} \times 365 \, \text{days} \times 158.987 \, \text{liters/barrel}
\]

Let's calculate this:

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

We'll find the answer in standard form.

#### b) **Percentage increase in oil production from 2022 to 2023**

We are given:
- Average production in 2022 = 1.685 million barrels/day = \(1.685 \times 10^6\) barrels/day
- Average production in 2023 = 1.794 million barrels/day = \(1.794 \times 10^6\) barrels/day

The percentage increase is calculated using the formula:
\[
\text{Percentage increase} = \left( \frac{\text{2023 production} - \text{2022 production}}{\text{2022 production}} \right) \times 100
\]
Substituting the values:
\[
\text{Percentage increase} = \left( \frac{1.794 - 1.685}{1.685} \right) \times 100
\]

We'll compute this percentage.

---

### Part 2: Gaute's Savings Account

#### a) **Amount in the account in five years**

We are given:
- Current amount = 105,607 kroner
- Fixed interest rate = 3.25% per year

To find the amount in five years, we use the compound interest formula:
\[
A = P(1 + r)^t
\]
where:
- \(A\) is the future amount,
- \(P\) is the principal (initial deposit),
- \(r\) is the annual interest rate (expressed as a decimal),
- \(t\) is the number of years.

First, we calculate how much will be in the account in five years starting from today, so \(t = 5\) and \(r = 0.0325\).

\[
A = 105,607(1 + 0.0325)^5
\]

We'll compute this value.

#### b) **Initial deposit five years ago**

Now we use the same formula for compound interest, but we solve for \(P\), the initial deposit, using the current amount as \(A\):

\[
105,607 = P(1 + 0.0325)^5
\]
Solving for \(P\):
\[
P = \frac{105,607}{(1 + 0.0325)^5}
\]

We'll calculate the initial deposit Gaute made five years ago.

---

Let me do the calculations now.### Part 1: Oil Production on the Norwegian Continental Shelf

#### a) Total oil production in 2023
The total oil production in 2023 was approximately:
\[
1.041 \times 10^{11} \text{ liters}
\]

#### b) Percentage increase from 2022 to 2023
The production increased by approximately:
\[
6.47\% 
\]

---

### Part 2: Gaute's Savings Account

#### a) Amount in the account in five years
In five years, Gaute will have approximately:
\[
123,920.46 \text{ kroner}
\]

#### b) Initial deposit five years ago
Gaute initially deposited approximately:
\[
90,000 \text{ kroner}
\]

---

Do you want more details or have any questions? Here are five related questions you could explore:

1. How many barrels of oil would 1.041 × 10¹¹ liters correspond to?
2. What would

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?

Calculate the total liters of oil produced in 2023 on the Norwegian continental shelf and determine the percentage increase in production from 2022 to 2023. Also, learn how to compute compound interest over 5 years with a fixed interest rate. Suitable for students in Grades 10-12.

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