Answer:
City A and city B will have equal population 25years after 1990
Step-by-step explanation:
Given
Let
years after 1990
population function of city A
population function of city B
<u>City A</u>
---- initial population (1990)
--- rate
<u>City B</u>
----- t = 10 in 2000
---- t = 20 in 2010
Required
When they will have the same population
Both functions follow exponential function.
So, we have:


Calculate the population of city A in 2000 (t = 10)





Calculate the population of city A in 2010 (t = 20)





From the question, we have:
and






Solve for B20


and
can be used to determine the function of city B

For: 
We have:


For: 
We have:


Divide
by 


Apply law of indices

--- (1)
Take 10th root of both sides
![1 + r_B = \sqrt[10]{2.2399}](https://tex.z-dn.net/?f=1%20%2B%20r_B%20%3D%20%5Csqrt%5B10%5D%7B2.2399%7D)

Subtract 1 from both sides

To calculate
, we have:

Recall that: 
So:



Hence:



The question requires that we solve for t when:

Where:




and

becomes

Divide both sides by 10000

Divide both sides by 


Take natural logarithm of both sides

Rewrite as:

Solve for t


Approximate
