Question

India's population has been catching up with China, with 1132 million in mid-2007 and growing at 1.6% per year, versus China then with 1318 million and growing at only 06%. If these rates continue, when will India have more people than China?

Answer 1

solve for t
1132 e^(.016t) = 1318 e^(.06t)

That will give you the time when they are equal.
You will have to use logs. (use ln)

Answer 2

Just noticed you have a typo, and I read it as .06

does it say 0.6 % ?
if so change my equation to

1132 e^(.016t) = 1318 e^(.006t)

You should get a t value of 15.2, add that to the year 2007 and draw your conclusion from that.