Leah investment is:
[tex]M_{\text{Leah}}=400_{}\cdot1.5^y[/tex]Where M is the ammount of money that she has, and y the number of years.
We want to know the number of years that must elapse for her investment to triple, so we want to know the value of y such that:
[tex]\begin{gathered} 3\cdot400=400\cdot(1+\frac{1.5}{100})^y \\ 3=(1.015)^y \\ \ln 3=y\cdot\ln (1.015) \\ y=\frac{\ln (3)}{\ln (1.015)}\cong73.788\cong73.79 \end{gathered}[/tex]It will take 73.79 years to triple her investment.
Lauren investment is:
[tex]M_{\text{Lauren}}=400\cdot(1+\frac{7}{8}\cdot\frac{1}{100})^m=400\cdot(1.00875)^{\frac{y}{12}}[/tex]Where M is the ammount of money that she has, and m the number of months, and y is the number of years.
We want to know the number of years that must elapse for her investment to triple, so we want to know the value of y such that:
[tex]\begin{gathered} 3\cdot400=400\cdot(1.00875)^{\frac{y}{12}} \\ 3=(1.00875)^{\frac{y}{12}} \\ \ln 3=\frac{y}{12}\ln (1.00875) \\ y=12\cdot\frac{\ln 3}{\ln (1.00875)} \\ y=1513.25 \end{gathered}[/tex]