I'd go by what the local DMV/State specifies.
Booster seats are for children who have outgrown convertible or toddler seats. Booster seats are for children who are four to eight years old, weigh 40 to 80 pounds, and are less than four feet, nine inches in height. You can use a booster seat until an adult seat belt correctly fits the child without use of the booster seat. Always use both the shoulder and lap belts with a booster seat. Never use only the lap belt with a booster seat.
TN law specifies (more fitting to your situation):
Children age four (4) through age eight (8), and measuring less than four feet nine inches (4'9") in height, must be secured in a belt-positioning booster seat system, meeting federal motor vehicle safety standards in the rear seat, if available, or according to the child safety restraint system or vehicle manufacturer's instructions. (Note: If the child is not between age four (4) and age eight (8), but is less than four feet nine inches (4'9") in height, he/she must still use a seat belt system meeting federal motor vehicle safety standards.)
Both results were found googling "booster seat [state]"