The annual amount of​ crude-oil production in a country​ (in millions of​ barrels) can be approximated by the function ​f(t)=1706(1.031)^t, where t= 8 corresponds to the year 2008. Find the amount of production in 2017 

We are given the function for crude-oil production:

\[
f(t) = 1706(1.031)^t
\]

where \( t = 8 \) corresponds to the year 2008. To find the year 2017 in terms of \( t \), note that the difference between 2017 and 2008 is 9 years. Thus:

\[
t = 8 + 9 = 17
\]

Now substitute \( t = 17 \) into the function to find the crude-oil production in 2017:

\[
f(17) = 1706(1.031)^{17}
\]

I'll calculate this value for you.The crude-oil production in 2017 is approximately 2866.66 million barrels.

Would you like more details or have any questions?

Here are 5 related questions to deepen your understanding:
1. How would the production change in 2025 using the same model?
2. What is the percentage increase in crude-oil production from 2008 to 2017?
3. How can we calculate the average annual growth rate using the function?
4. What would happen to the production if the growth rate was reduced to 1.02 instead of 1.031?
5. How do exponential growth models like this one compare to linear growth models in long-term predictions?

**Tip:** Exponential growth models like this can quickly produce very large numbers due to the compounding effect. Always check if the growth rate is sustainable for long-term forecasting.

The annual amount of crude-oil production in a country (in millions of barrels) can be approximated by the function f(t) = 1706(1.031)^t, where t = 8 corresponds to the year 2008. Find the amount of production in 2017.

Learn how to calculate crude oil production in 2017 using the exponential growth model f(t) = 1706(1.031)^t. This problem explores exponential functions and their applications in real-world scenarios. Suitable for students in Grades 10-12.

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