Solution:
The growth rate is given below as
[tex]r=2.3\%[/tex]The initial population is
[tex]P_0=832[/tex]The exponential growth formula is given below as
[tex]\begin{gathered} P=P_0(1+r)^t \\ 832(1+\frac{2.3}{100})^t=1500 \\ 832(1.023)^t=1500 \\ (1.023)^t=\frac{1500}{832} \\ (1.023)^t=1.803 \\ take\text{ ln of both sides} \\ ln(1.023)^t=ln(1.803) \\ tln(1.023)=ln(1.803) \\ t=\frac{ln(1.803)}{ln(1.023)} \\ t=25.9years \\ \end{gathered}[/tex]Hence,
The final answer is
The population will exceed 1500 in approximately 26 years' time
