What is the right formula for exponential growth?

Question

I watched a video on Virtual Nerd about exponential growth. The problem is "In year 2000, the population in a place was 100. If it grows at a rate of 30% annually, what will the population be in 2020?". they used the formula P=a(1+r)^t. They got approximately 19,005. But when I tried to use the formula for Growth Law: y=ae^kt, I got approximately 40,343. I don't know if the way I use the formula is right or the formula itself cannot be used or..I don't know. Please help me.

Answer 1

The answer given 19005 is correct and the formula is correct.

 

If you use y = ae^kt, you must set e^k = 1.3, which is exactly the same as the other formula.

Answer 2

Here is another way to look at it:

 

At the end of any year, the population is 30% higher than it was at the start of the year.  That means it is 1.30 times as much.  If you start with an initial population of P₀ and keep this up for t years, you get

 

P(t) = P₀(1.30)^t

 

Since you started at year 2000 and went up to year 2020, t = 20 years.

 

P(20) = 100(1.30)²⁰ ≅ 19,005