Final answer:
The AWS service suitable for deploying a MySQL database that requires scalability and automatic backup is Amazon RDS, as it provides easy setup, operation, and scaling as well as automated administrative tasks including backups.
Step-by-step explanation:
For a company that is deploying a MySQL database on AWS and requires both scalability and automatic backup, the suitable service to use would be Amazon RDS (Amazon Relational Database Service). Amazon RDS makes it easy to set up, operate, and scale a relational database in the cloud. It provides cost-efficient and resizable capacity while automating time-consuming administration tasks such as hardware provisioning, database setup, patching, and backups. It also supports scaling of compute resources or storage capacity with only a few mouse clicks or an API call.
Amazon S3 is object storage for storing and retrieving any amount of data, and is not a database service. Amazon EC2 provides scalable computing capacity in the cloud, but requires manual management and scaling of the database. Amazon DynamoDB is a NoSQL database service that provides fast and predictable performance with seamless scalability but does not support MySQL.