class_docstr: Class for the Fisher information metric on exponential distributions.
  
  References
  ----------
  .. [AM1981] Atkinson, C., & Mitchell, A. F. (1981). Rao's distance measure.
      Sankhyā: The Indian Journal of Statistics, Series A, 345-365.
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docstr: Generate parameterized function for geodesic curve.
  
  Parameters
  ----------
  t : array-like, shape=[n_times,]
      Times at which to compute points of the geodesics.
  
  Returns
  -------
  geodesic : array-like, shape=[..., n_times, 1]
      Values of the geodesic at times t.
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code: def _geodesic_path(t, initial_point, base):
      """Generate parameterized function for geodesic curve.
  
      Parameters
      ----------
      t : array-like, shape=[n_times,]
          Times at which to compute points of the geodesics.
  
      Returns
      -------
      geodesic : array-like, shape=[..., n_times, 1]
          Values of the geodesic at times t.
      """
      t = gs.reshape(gs.array(t), (-1,))
      base_aux, t_aux = gs.broadcast_arrays(base, t)
      return gs.expand_dims(initial_point * base_aux**t_aux, axis=-1)
  
imports: from scipy.stats import expon
  import geomstats.backend
  from geomstats.geometry.base import VectorSpaceOpenSet
  from geomstats.geometry.euclidean import Euclidean
  from geomstats.geometry.riemannian_metric import RiemannianMetric
  from geomstats.information_geometry.base import InformationManifoldMixin, ScipyUnivariateRandomVariable
label_desc: Use image node_id 3 for calling the ExponentialMetric obj's underlying member method code with example usage: obj._geodesic_path(t, initial_point, base) and returns: gs