Final answer:
The domain of the vector function is (-∞, ∞) in interval notation.
Step-by-step explanation:
The domain of a vector function consists of all the possible values that the input variable (in this case, 't') can take. In order to find the domain of the given vector function, we need to determine the values of 't' for which the function is defined. In this case, the vector function is defined for all real numbers, since there are no restrictions on the values of 't' in the given function.
Therefore, the domain of the vector function r(t) = 36 - t², e⁽⁻⁵ᵗ⁾, ln(t⁴) is (-∞, ∞) in interval notation, which includes all real numbers.