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

Albarellak 2021-08-14 Answered
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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Expert Answer

Elberte
Answered 2021-08-15 Author has 17801 answers

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

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