Answer:
Remember the relation:
Ln(a^x) = x*ln(a)
In 1969, the club had 20,000 members, and it grew an average of 6.4% (or 0.064 in decimal form, this is the one we will use) per year.
This means that in 1970, the club had:
20,000 + (0.064)*20,000 = (1.064)*20,000
In 1971, the club had:
(1.064)*20,000 + 0.064*(1.064)*20,000 = (1.064)^2*20,000 members.
Already you can see a pattern, N years after 1969, the club will have:
M(N) = (1.064)^N*20,000 members
Now we want to find the number N such that:
M(N) = 50,000 = (1.064)^N*20,000
Let's solve this for N.
50,000 = (1.064)^N*20,000
50,000/20,000 = (1.064)^N
5/2 = (1.064)^N
Now we apply Ln( ) in both sides
ln(5/2) = ln( (1.064)^N) = N*ln( 1.064)
N = ln(5/2)/ln( 1.064) = 14.8
Then will pass 14.8 years (since 1969) to reach the 50,000 members
