# Given: A=Pe^(rt) A=3P Find t if r is: a) 2% b) 4% c) 6% d) 8% e) 10%

Given:
$$\displaystyle{A}={P}{e}^{{{r}{t}}}$$
$$\displaystyle{A}={3}{P}$$
Find t if r is:
a) 2%
b) 4%
c) 6%
d) 8%
e) 10%
f) 12%

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Elberte

$$\displaystyle{A}={P}{e}^{{{r}{t}}}$$
$$\displaystyle{A}={3}{P}$$
$$\displaystyle{3}{P}={P}{e}^{{{r}{t}}}$$
$$\displaystyle{3}={e}^{{{r}{t}}}$$
$$\displaystyle \ln{3}={r}{t}$$
$$\displaystyle{t}=\frac{{\ln{3}}}{{r}}$$
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) $$\displaystyle{t}=\frac{{\ln{3}}}{{1.2}}\approx{9.2}$$