Chappell Roan's "HOT TO GO!" was released August 11, 2023. Three months after being released (𝑡=3), it could be found on 58 spotify playlists. Ten months after being released (𝑡=10), it could be found on 338 Spotify playlists. Let 𝑁𝑡 be a function that includes both of the given data points to model how many Spotify playlists included "HOT TO GO!" 𝑡 months after the song was released.
(i) Use the given data to find the average rate of change of 𝑁𝑡, in playlists per month, from 𝑡=3 to 𝑡=10. Express your answer as a decimal approximation.
(ii) Use the average rate of change found in (i) to estimate the number of Spotify playlists that contained "HOT TO GO!" twelve months after the song's release.