The amount of money in the savings account 't' years after 2015 is given by,
[tex]P(t)=100\times(10)^{0.007t^{}}[/tex]Solve for P(0) as,
[tex]P(0)=100\times(10)^{0.007\times0}=100\times10^0=100\times1=100[/tex]It means, at the beginning of the tenure, i. e. year 2015, the account had $100 only.
The time taken for the account to have $140 is calculated as,
[tex]\begin{gathered} P(t)=140 \\ 100\times(10)^{0.007t}=140 \\ 10^{0.007t}=1.4 \end{gathered}[/tex]Take common logarithms on both sides,
[tex]\begin{gathered} \ln ^{}_{10}10^{0.007t}=\ln _{10}1.4 \\ 0.007t\times\ln _{10}10=0.146 \\ 0.007t\times1=0.146 \\ t=\frac{0.146}{0.007} \\ t\approx21 \end{gathered}[/tex]Thus, it will take arount 21 years for the account to have $140.
