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

Answer:
13. A
14. C.
Step-by-step explanation:
A relation is a function if there is only one y assigned to each x.
That is if you have a set of points, there should be no repeated x value.
So looking at {(0,0),(-2,4),(-2,-4),(-3,7)} this is not a function because you have two x's that are the same. A.
The slope-intercept form of a linear equation is y=mx+b where m is the slope and b is the y-intercept.
The y-intercept is where the graph goes through the y-axis at. It goes through at -1 so b=-1.
The slope is rise/run. So starting from the y-intercept (0,-1) we need to find another point to count the rise & run to... How about (3,1)? That works. You can do the counting if you want. You could also use the slope formula.
To use the slope formula, I just like to line the points up vertically and subtract vertically then put 2nd difference over the 1st difference.
(0,-1)
-(3,1)
--------
-3 -2
So the slope is -2/-3 or just 2/3.
So the equation is y=2/3 x-1
C.
Answer:

Step-by-step explanation:
Area of a Circle: 
The r is the length of the radius of the circle
The radius of the shown circle is 9 m


Answer:
m³n
Step-by-step explanation:
Triangle ABC is an isosceles triangle.
Solution:
Given data:
∠ABC = 70° and ∠ACD = 55°
<em>If two parallel lines are cut by a transversal, then alternate interior angles are congruent.</em>
m∠BAC = m∠ACD
m∠BAC = 55°
<em>Sum of the angles in a straight line add up to 180°.</em>
m∠ACD + m∠ACB + m∠ABC = 180°
55° + m∠ACB + 70° = 180°
m∠ACB + 125° = 180°
Subtract 125° from both sides, we get
m∠ACB = 55°
In triangle ABC,
∠BAC = 55° and ∠ACB = 55°
∠BAC = ∠ACB
Two angles in the triangle are equal.
Therefor triangle ABC is an isosceles triangle.