Population growth is not exponential but actually slowing. This is one of many misconceptions about demographics - an absolutely fascinating and important subject which gets little attention in the media or schools.
Here's a nice intro from Joel Cohen, a longtime leader in the field:
The rate may be slowing (as expected), but the overall rate has been exponential until now. Like it took us forever to get to 1 billion, but getting to 7 billion took no time at all from that point.
If the growth rate is slowing it is not exponential - a constant growth rate is the definition of exponential[1].
After increasing dramatically during the first half of the 20th century the growth rate has declined for the last 40 years. Looking more deeply into the demographics (by country and age group) it is pretty clear that this decline will continue for many decades to come. The video I linked above goes into some of this.
Most experts currently predict that the world's population will peak (i.e. below zero population growth) middle of this century around 9 billion - although a few say as high as 11 billion or as low as 7 billion. These predictions are way down from just a decade ago.
Here's a nice intro from Joel Cohen, a longtime leader in the field:
http://www.floatinguniversity.com/lectures-cohen