I did some experimentation on how approval rating affects the growth rate, and here is what I found.
My home planet's population of 8 billion increased by the following when:
My approval rating at 100% = population increased by .15b
My approval rating between 76% and 99% = population increased by .08b to .09b
My approval rating between 41% and 75% = population increased by .06b to .07b
My approval rating between 20% and 40% = population stayed the same
My approval rating less than 20% = population decreased.
When I created a custom race and spent 6 points to get the 70% growth bonus, I discovered it really wasn't 70%:
My approval rating at 100% = population increased by .25b
My approval rating between 76% and 99% = population increased by .16b
My approval rating between 41% and 75% = population increased by .13b
My approval rating between 20% and 40% = population stayed the same
My approval rating less than 20% = population decreased.