The population of Boomtown is 475,000 and is increasing at a rate of 3.75% each year.When will the population exceed 1 million people (to the nearest year)?
Answers
It would take 21 years for the population of Boomtown to reach 1 million people.
An exponential growth is in the form:
y = abˣ;
where y, x are variables, a is the initial value of y and b is > 1
Let y represent the population of Boomtown after x years.
Given that initially there is a population of 475,000, hence a = 475000. Also, it is increasing at a rate of 3.75%, hence b = 100% + 3.75% = 1.0375
Hence:
y = 475000(1.0375)ˣ
For a population of 1000000:
1000000 =475000(1.0375)ˣ
2.1 = (1.0375)ˣ
xln(1.0375) = ln(2.1)
x = 21 years
Hence it would take 21 years for the population of Boomtown to reach 1 million people.
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After 20.22 years the population exceed 1 million people, if the population of Boomtown is 475,000 and is increasing at a rate of 3.75% each year.
Step-by-step explanation:
The given is,
Population of Boomtown is 475,000
Increasing at a rate of 3.75% each year
After few years population exceed 1 million people
Step:1
Formula to calculate population with a given rate of increase,
..............................(1)
Where,
F - Population after t years
P - Population at initial
r - Rate of increase
t - No.of years
From the given values,
F = 1000000
P = 475,000
r = 3.75%
Equation (1) becomes,
Take log on both sides,
Substitute log values,
= 20.2216
t ≅ 20.222 years
Result:
After 20.22 years the population exceed 1 million people, if the population of Boomtown is 475,000 and is increasing at a rate of 3.75% each year.
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Answer:
The total surface area of all 6 prisms is 6336 in^2.
Step-by-step explanation:
Let's find the surface area of ONE prism and then multiply that result by 6 to obtain the final answer.
One prism:
The area of the two 13 in by 26 in rectangular tabs is 2(13 in)(26 in), or 676 in^2 (subtotal);
The area of the two triangles of base 10 in and height 12 in is 2([1/2][10 in][12 in], or 120 in^2; and, finally,
The area of the 10 in by 26 in base is 260 in^2.
The total surface area of ONE prism is thus:
676 in^2 + 120 in^2 + 260 in^2, or 1056 in^2.
Now, because there are 6 of these prisms, multiply this last result by 6:
6(1056 in^2) = 6336 in^2.
The total surface area of all 6 prisms is 6336 in^2.
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II
III
IV
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The number 6 - 8i is located in the thirdquadrant of the complex plane.
Option C is the correct answer.
What are quadrants?
The term "quadrants" usually refers to the four regions of the Cartesian plane, which is a two-dimensional coordinate system.
The plane is divided into four regions called quadrants, labeled I, II, III, and IV, which are numbered counterclockwise starting from the upper right quadrant (I).
Quadrant I: The point has positive x and positive y coordinates.
Quadrant II: The point has negative x and positive y coordinates.
Quadrant III: The point has negative x and negative y coordinates.
Quadrant IV: The point has positive x and negative y coordinates.
We have,
To determine the quadrant where the complexnumber 6 - 8i is located, we need to consider the signs of the real and imaginary parts of the number.
The realpart of the number is 6, which is positive, indicating that the number lies to the right of the origin.
The imaginarypart of the number is -8i, which is negative, indicating that the number lies below the origin.
Therefore,
The number 6 - 8i is located in the thirdquadrant of the complex plane.
Learn more about quadrants here:
#SPJ7
Answer:
IV
Step-by-step explanation:
The 6 is to the right of the x axis ( positive x) and the -8i is below the x axis to the right.
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1 meter = 1000 millimeters.
100 x 1000 = 1000000 millimeters.
Answers
Second step: If there is 2 of the same number that repeats just put that number in the front of the resulting radical
Third: Just multiply the remaining radicals together and put the number in front of it.
Now you have
Step 1: Find the prime factorization of the number inside a radical.252 = 2 x 2 x 3 x 3 x 7
Step 2: Determine the index of the radical. In this case, the index is two because it is a square root, which means we need two of a kind.√252 = √2 x 2 x 3 x 3 x 7
Step 3: Move each group of numbers or variables from inside the radical to outside the radical. In this case, the pair of 2’s and 3’s moved outside the radical.2 x 3√7
Step 4: Simplify the expressions both inside and outside the radical by multiplying.6√7
Hope that was clear!