The annual amount of​ crude-oil production in a country​ (in millions of​ barrels) can be approximated by the function ​f(t)equals1721 left parenthesis 1.058 right parenthesis Superscript t​, where tequals8 corresponds to the year 2008.
​(a) Find the amount of production in 2018.
​(b) If the trend​ continues, find the amount of production in 2027.
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Part 1
​(a) The amount of production in 2018 was 
  
enter your response here million barrels.
​(Round to the nearest whole number as​ needed.) 

The function for crude oil production is given as:

\[
f(t) = 1721 \times (1.058)^t
\]

where \( t = 8 \) corresponds to the year 2008. To find the amount of production in different years, we need to calculate \( t \) for those years based on this reference.

### Part (a) - Find the amount of production in 2018:

To find \( t \) for the year 2018:
\[
t = 2018 - 2008 = 10
\]

Now, substitute \( t = 10 \) into the function:

\[
f(10) = 1721 \times (1.058)^{10}
\]

Let's calculate that.

\[
f(10) = 1721 \times 1.7456 \approx 3004.15
\]

Rounding to the nearest whole number, the amount of production in 2018 is approximately **3004 million barrels**.

### Part (b) - Find the amount of production in 2027:

To find \( t \) for the year 2027:
\[
t = 2027 - 2008 = 19
\]

Now, substitute \( t = 19 \) into the function:

\[
f(19) = 1721 \times (1.058)^{19}
\]

Let's calculate that.

\[
f(19) = 1721 \times 2.8228 \approx 4858.57
\]

Rounding to the nearest whole number, the amount of production in 2027 is approximately **4859 million barrels**.

Would you like more details or have any questions?

Here are some related questions:
1. How would the formula change if the growth rate were different?
2. What is the percentage increase in production from 2018 to 2027?
3. How would you find the year when production reaches 5000 million barrels?
4. What would happen if the annual growth rate decreased to 3%?
5. Can you model a scenario where the growth rate starts decreasing every year?

**Tip:** When rounding to the nearest whole number, make sure you check the first decimal place (if it's 5 or above, round up).

The annual amount of crude-oil production in a country (in millions of barrels) can be approximated by the function f(t) = 1721(1.058)^t, where t = 8 corresponds to the year 2008. (a) Find the amount of production in 2018. (b) If the trend continues, find the amount of production in 2027.

Explore how to calculate crude-oil production using an exponential growth model. Learn step-by-step how to find the production in 2018 and 2027 using the given function f(t) = 1721(1.058)^t, with t = 8 corresponding to the year 2008. Suitable for high school students in Grades 9-12.

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