\(\displaystyle{A}={P}{e}^{{{r}{t}}}\)

\(\displaystyle{A}={3}{P}\)

\(\displaystyle{3}{P}={P}{e}^{{{r}{t}}}\)

\(\displaystyle{3}={e}^{{{r}{t}}}\)

\(\displaystyle \ln{3}={r}{t}\)

\(\displaystyle{t}=\frac{{\ln{3}}}{{r}}\)

Substitute r to solve:

a) \(\displaystyle{t}=\frac{{\ln{3}}}{{0.02}}\approx{54.9}\)

b) \(\displaystyle{t}=\frac{{\ln{3}}}{{0.04}}\approx{27.5}\)

c) \(\displaystyle{t}=\frac{{\ln{3}}}{{0.06}}\approx{18.3}\)

d) \(\displaystyle{t}=\frac{{\ln{3}}}{{0.08}}\approx{13.7}\)

e) \(\displaystyle{t}=\frac{{\ln{3}}}{{0.1}}\approx{11}\)

f) \(\displaystyle{t}=\frac{{\ln{3}}}{{1.2}}\approx{9.2}\)