Alan

Always good to have a couple of different approaches (even better when they give the same answers!).

Let the initial size be N₀.

After 8 years N = 2*N₀.

After 2*8 =16 years N = 2*2*N₀ = 4N₀.

After 4*8 = 32 years N = 2*4*N₀ = 8N₀.

After 8*8 = 64 years N = 2*8*N₀ = 16N₀.

So it seems like the pattern is:

After n*8 years N = 2*n*N₀.

When n*8 = 40, we can see that n must be 5 (since 5*8 = 40) and we are told N = 100,000 so:

100000 = 2*5*N₀.

N₀ = 100000/10 or N₀ = 10,000

10 years from now is 50 years from the start, so n*8 = 50, n = 50/8

N = 2*(50/8)*10000 = 125,000

If we are keeping to the Real numbers only, then log(x-8) isn't defined unless x is strictly greater than 8, so Chris is correct in this situation.

However, if we allow Complex numbers then we have log(x^2-64) - log(x-8) = log(x+8) + log(x-8) - log(x-8) = log(x+8) for all x except x = -8 and x = 8.

GoldenLeaf, you put 4(20) instead of 4(25) for 4t² when you started to fill in the missing values!

Look for the prime factors of 45.  These are 3*3*5  or 3²*5.

This means √45 = √(3²*5) = √(3²)*√5 or 3√5

This will depend on the nature of the function.  An infinite number of different functions will have f(-3) = 5