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
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