Let's break down how to project the GDP for Country A using the given equation:

Country A's GDP function is:

$f(x) = 0.00006(1.102)^x$

Part 1: How to find the projected GDP in 2018

To find the projected GDP in 2018, note that $x = 60$ corresponds to 1960. The year 2018 is 58 years after 1960. So:

$x = 60 + 58 = 118$

Thus, we substitute $x = 118$ into the function $f(x)$ to find the projected GDP:

$f(118) = 0.00006(1.102)^{118}$

So, Choice A is correct: "To find the projected GDP in 2018, substitute 118 for $x$ and evaluate to find $f(x)$."

Part 2: Projected GDP in 2018

Now, let's compute the GDP in 2018 using the formula:

$f(118) = 0.00006 \times (1.102)^{118}$

Calculating this will give the projected GDP in trillions of dollars. (I can calculate this for you if you'd like.)

Part 3: How to find the projected GDP in 2034

To find the projected GDP in 2034, we calculate the corresponding $x$-value. The year 2034 is 74 years after 1960, so:

$x = 60 + 74 = 134$

Thus, we substitute $x = 134$ into the function $f(x)$ to find the projected GDP:

$f(134) = 0.00006(1.102)^{134}$

So, Choice B is correct: "To find projected GDP in 2034, substitute 134 for $x$ and evaluate to find $f(x)$."

Would you like me to compute the actual values for the projected GDPs in 2018 and 2034?

Relative questions:

1. How would the projected GDP change if the growth rate of 1.102 were different?
2. Can we use the same method to estimate the GDP for earlier years, such as 1950?
3. How do small changes in the exponent affect the long-term GDP projection?
4. How would the projection differ for Country B using the same years?
5. What are the real-world factors that could make the GDP deviate from these projections?

Tip: Exponential growth models, like the one used here, can significantly overestimate values if growth rates are not adjusted for real-world conditions like inflation and economic shocks.