I don’t have the charts the question refers to, but here’s how you work out the answer.
Your principal is $2000 and you want to grow it to $5000 in 15 years. So the growth you want is 5000/2000=2.5. To find the interest rate that would give you the amount you want you need to take the 15th root of 2.5, assuming interest is compounded annually—just once a year. You will need a calculator to do this. It comes to about 1.063. Now subtract 1, to get 0.063 then multiply by 100, to get 6.3%. That’s the compound interest rate you need.
The chart above shows interest rates on the horizontal axis up to about 9%. The curves are colour-coded according to the number of years: red=5 yrs, blue=10 yrs, green=15 yrs, purple=20 yrs, black=25 yrs. You want the green curve. And the growth value is 5000/2000=2.5. You can see that when growth=2.5 on the green line, the corresponding rate is about 6.3%.