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.

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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.

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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!