Could you please help me with this difficult question.

It is estimated that the population, N, of two towns, Princetown (P) and Queensbridge (Q) will increase according to the law:

N=A10^(kt) where t is the number of years reckoned from 1994

If their populations were:

P: 20 000 in 1994 and 26 400 in 1997
Q: 10 000 in 1994 and 11 560 in 1997

a) Calculate the values of the constant A and k
b) What will be the population of P in the year 2010?
c) During what year will the population of Q double?

for a) you can use the case where t = 0 to get a value for A, then you can use the case where t > 0 to find out the value of k.

for b) once you know A and k it's trivial to put in the right t.

for c) you need to find t where \frac{N(t)}{N(t-1)} \ge 2 you should be able to easily derive an expression that gives you t.

Thank you very much appreciated

But I didn't quite understand part a)
I'm sorry

Okay so for Q we have N=A10^(kt), t = 0, N = 10000

so you can solve 10000 = A10^(0k) = A10^0

There's only 1 variable, A, so you can work out it's value.

Now you put your value for A into the equation with the 2nd t value for which you have a value of N. Then you will have k as the only variable. And you can solve to find it.

Ok cool
WOW you respond quickly
Thanks

Sorry again but what is the variable of A and then of k
I did the working out but came up weird and wrong answers.
I know this must be frustrating but yeah...
Thanks again last time

For P:

N = A10^{kt}

20000 = A10^0k

A = 20000

N = A10^{kt}

26400 = 20000*10^{3k}

10^{3k} = \frac{26400}{20000}

3k = log_{10}(\frac{26400}{20000})

3k = log_{10}(1.32)

3k \approx 0.121

k \approx 0.0402

I've got everything you explained so far...
With b) being 87948.8 I think

But I don't know c) even after you explained it to me