the annual amount of energy produced in a country from dry natural gas (in trillion cubic feet) can be approximated by.the function. g(t)= 16.8(1.026)^t, where t = 10 corresponds to the year 2010. Find the amout of dry natural gas energh produced in 2022

The given function approximates the annual amount of energy produced from dry natural gas in trillion cubic feet, where \( g(t) = 16.8(1.026)^t \) and \( t = 10 \) corresponds to the year 2010. To find the amount of energy produced in 2022, we need to first determine the value of \( t \) for 2022.

### Step 1: Calculate \( t \) for 2022
Since \( t = 10 \) corresponds to 2010, we can calculate the value of \( t \) for 2022 as follows:
\[
t = 10 + (2022 - 2010) = 10 + 12 = 22
\]

### Step 2: Plug \( t = 22 \) into the function \( g(t) \)
Now substitute \( t = 22 \) into the function:
\[
g(22) = 16.8(1.026)^{22}
\]

### Step 3: Calculate \( g(22) \)
First, calculate \( (1.026)^{22} \):
\[
(1.026)^{22} \approx 1.741
\]
Now multiply by 16.8:
\[
g(22) = 16.8 \times 1.741 \approx 29.25
\]

### Conclusion:
The amount of dry natural gas energy produced in 2022 is approximately **29.25 trillion cubic feet**.

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

Here are 5 related questions to expand this information:
1. How would the energy production change for a different year, such as 2025?
2. What is the growth rate of energy production from dry natural gas?
3. How does this growth compare to other energy sources, such as renewable energy?
4. What are the environmental impacts of increasing natural gas production at this rate?
5. How does the function \( g(t) = 16.8(1.026)^t \) compare to a linear growth model?

**Tip:** Exponential growth functions like this one can quickly lead to large increases over time due to compounding effects.

The annual amount of energy produced in a country from dry natural gas (in trillion cubic feet) can be approximated by the function g(t)= 16.8(1.026)^t, where t = 10 corresponds to the year 2010. Find the amount of dry natural gas energy produced in 2022.

This problem demonstrates how to calculate the amount of energy produced from dry natural gas in 2022 using the exponential growth function g(t) = 16.8(1.026)^t. Learn how to solve this using key algebraic concepts and exponential properties. Suitable for students in Grades 10-12.

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