Answer: D - 6 months
Step-by-step explanation:
It is given that,
The current number of members = 530,
Monthly rate of increasing members = 8 %,
Let after x months the number of members will 850,
Thus, we can write,
[tex]530(1+\frac{8}{100})^x=850[/tex]
[tex]530(1+0.08)^x=850[/tex]
[tex]1.08^x=\frac{850}{530}[/tex]
[tex]x log(1.08) = log(1.60377358)\implies x =\frac{log(1.60377358)}{log(1.08)}=6.13764228\approx 6[/tex]
Thus, About in 6 months the number of members will 850.
