Answer:
[tex]x=31.32\text{Thousandyears}[/tex]
Explanation: We have to find the number of years that it would take for the population to reach 700 thousand, the step by step calculations are as follows:
[tex]\begin{gathered} P(x)=200e^{(0.04x)} \\ 700=200e^{(0.04x)} \\ e^{(0.04x)}=\frac{700}{200}=\frac{7}{2}=3.5 \\ 0.04x=ln(3.5) \\ x=\frac{ln(3.5)}{0.04}=\frac{1.2527629685}{0.04}=31.3190742124 \\ x=31.3190742124 \\ x=31.32\text{ Thousand years.} \end{gathered}[/tex]
Therefore the answer is, it would take 31.32 thousand years for the population to reach 700 thousand.
