Question

The exports of goods of a country, \( G = G(t) \), has a growth rate of \( a/t \), and its exports of services, \( S = S(t) \), has a growth rate of \( b/t \). What is the growth rate of its total exports \( X \)?

• A. \( \frac{a}{t} + \frac{b}{t} \)
• B. \( \frac{a}{G} + \frac{b}{S} \)
• C. \( \frac{a+b}{G+S} \)
• D. \( \frac{Ga + Sb}{tX} \)

Hint:

The growth rate of total exports is the sum of the individual growth rates of goods and services.

Answer 1

The Correct Option is A

Let the total exports \( X \) be the sum of exports of goods and services, i.e., \[ X = G + S \] We are given that: - The growth rate of exports of goods is \( a/t \) - The growth rate of exports of services is \( b/t \) The growth rate of total exports \( X \) is simply the sum of the growth rates of goods and services. Therefore, the growth rate of total exports is: \[ \frac{a}{t} + \frac{b}{t} \] Final Answer: \[ \boxed{\frac{a}{t} + \frac{b}{t}} \]