Answer: $363$

Explanation:1. Understand the function: The function $g(t) = 294 + (363 - 294)(2.72)^{-0.103t}$ gives the approximate temperature of the liquid $t$ minutes after the beaker was placed on the table.

2. Determine the time when the beaker was placed on the table: "When the beaker was placed on the table" corresponds to the initial time, which is $t=0$ minutes.

3. Calculate the temperature at $t=0$: Substitute $t=0$ into the function $g(t)$: $g(0) = 294 + (363 - 294)(2.72)^{-0.103 \times 0}$ $g(0) = 294 + (363 - 294)(2.72)^0$

4. Simplify the expression: Any non-zero number raised to the power of $0$ is $1$. So, $(2.72)^0 = 1$. The difference $(363 - 294)$: $363 - 294 = 69$. So, $g(0) = 294 + (69)(1)$ $g(0) = 294 + 69$ $g(0) = 363$

5. Conclusion: According to this function, the approximate temperature, in kelvins, of the liquid when the beaker was placed on the table was $363$ kelvins.