The only time exponential backoff is useful is if the failure is due to a rate limit and you specifically need a mechanism to reduce the rate at which you are attempting to use it.
In the common case that the thing you're trying to talk is just down, exponential backoff with base N (e.g. wait 2x longer each time) increases your expected downtime by a factor of N (e.g. 2), because by the time your dependency is working again, you may be waiting up to the same amount of time again before you even retry it! Meanwhile, your service is down and your customers can't use it and your program is doing nothing but sleeping for another 30 minutes before it even checks to see if it can work.
And for what? What is the downside to you if your program retries much more frequently?
I much prefer setting a fixed time period to wait between retries (would you call that linear backoff? no backoff?), so for example if the thing fails you just sleep 1 second and try again, forever. And then your service is working again within 1 second of your dependency coming back up.
If you really must use exponential backoff then pick a quite-low upper bound on how long you'll wait between retries. It is extremely frustrating to find out that something wasn't working just because it was sleeping for a long time because the previous handful of attempts failed.