The annual amount of​ crude-oil production in a country​ (in millions of​ barrels) can be approximated by the function ​f(t)equals1712 left parenthesis 1.051 right parenthesis Superscript t​, where tequals8 corresponds to the year 2008.
​(a) Find the amount of production in 2014.
​(b) If the trend​ continues, find the amount of production in 2025.
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Part 1
​(a) The amount of production in 2014 was

enter your response here million barrels.
​(Round to the nearest whole number as​ needed.)

The given crude-oil production function is:

\[
f(t) = 1712 \times (1.051)^t
\]

where \(t = 8\) corresponds to the year 2008.

### (a) Finding the amount of production in 2014:

First, determine the value of \(t\) for the year 2014. Since \(t = 8\) corresponds to the year 2008, for 2014:

\[
t = 2014 - 2000 = 14
\]

Now, substitute \(t = 14\) into the function:

\[
f(14) = 1712 \times (1.051)^{14}
\]

Let me calculate this.

The amount of crude-oil production in 2014 was approximately **3435 million barrels**, rounded to the nearest whole number.

### (b) Finding the amount of production in 2025:

To find the amount of production in 2025, we need to calculate \(t\) for the year 2025. Since \(t = 8\) corresponds to 2008:

\[
t = 2025 - 2000 = 25
\]

Now, we substitute \(t = 25\) into the function:

\[
f(25) = 1712 \times (1.051)^{25}
\]

Let me calculate this as well.The amount of crude-oil production in 2025 is projected to be approximately **5937 million barrels**, rounded to the nearest whole number.

Would you like more details or have any questions about this? 

Here are five related questions to explore further:

1. How would changes in the growth rate affect future oil production?
2. What would be the production amount if the growth rate dropped to 3% annually?
3. How much oil would have been produced in 2010 using the given model?
4. Can we model other commodities' production using similar functions?
5. What would the production be in 2030 if the growth trend continues?

**Tip:** Exponential functions are often used to model growth processes where a fixed percentage increase occurs over time.

The annual amount of crude-oil production in a country (in millions of barrels) can be approximated by the function f(t) = 1712 (1.051)^t, where t = 8 corresponds to the year 2008. (a) Find the amount of production in 2014. (b) If the trend continues, find the amount of production in 2025.

Learn how to calculate crude-oil production in a country using the exponential growth function f(t) = 1712(1.051)^t. This problem demonstrates how to find production amounts for 2014 and 2025. Suitable for high school students studying exponential functions and growth models.

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