1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
almond37 [142]
2 years ago
7

In 2018, the population will grow over 700,000.The population of a city in 2010 was 450,000 and was growing at a rate of 5% per

year. In what year will the population be over 700,000? Show all work.
Mathematics
1 answer:
Firlakuza [10]2 years ago
8 0

Answer:

The year is 2020.

Step-by-step explanation:

Let the number of years passed since 2010 to reach population more than 7000000 be 'x'.

Given:

Initial population is, P_0=450,000

Growth rate is, r=5\%=0.05

Final population is, P=700,000

A population growth is an exponential growth and is modeled by the following function:

P=P_0(1+r)^x

Taking log on both sides, we get:

\log(P)=\log(P_0(1+r)^x)\\\log P=\log P_0+x\log (1+r)\\x\log (1+r)=\log P-\log P_0\\x\log(1+r)=\log(\frac{P}{P_0})\\x=\frac{\log(\frac{P}{P_0})}{\log(1+r)}

Plug in all the given values and solve for 'x'.

x=\frac{\log(\frac{700,000}{450,000})}{\log(1+0.05)}\\x=\frac{0.192}{0.021}=9.13\approx 10

So, for x > 9.13, the population is over 700,000. Therefore, from the tenth year after 2010, the population will be over 700,000.

Therefore, the tenth year after 2010 is 2020.

You might be interested in
Supplementary angles are two angles whose measures have a sum of 180∘. What is the value of x? Write and solve an equation for x
Evgen [1.6K]
I is a good friend and a good uuuuuuyyuyhyyytfikh..
8 0
2 years ago
What is a simple way to solve for the sum and difference of 2 cubes? For example, 27+64<img src="https://tex.z-dn.net/?f=x%5E3"
salantis [7]

Answer:

(3 + 4x)(9 - 12x + 16x²) = 0

(4m - 1)(16m² + 4m + 1) = 0

Step-by-step explanation:

Here we have to solve the sum of two cubes which is 27 + 64x^{3}

Now, the equation is 27 + 64x^{3} = 0

⇒ 3³ + (4x)³ = 0

⇒ (3 + 4x)[3² - 3(4x) + (4x)²] = 0

⇒ (3 + 4x)(9 - 12x + 16x²) = 0

So, (3 + 4x) = 0 or (9 - 12x + 16x²) = 0

Therefore, from the above two relation we can solve for x.

One root will be - \frac{3}{4} and the others we will get by applying Sridhar Acharya Formula, which will give a pair of conjugate imaginary roots of the equation.  

Again, we have to solve the difference of two cubes which is 64m^{3} - 1

Now, the equation is 64m^{3} - 1 = 0

⇒ (4m)³ - 1³ = 0

⇒ (4m - 1)[(4m)² + 4m(1) + 1²] = 0

⇒ (4m - 1)(16m² + 4m + 1) = 0

So, (4m - 1) = 0 or (16m² + 4m + 1) = 0

Therefore, from the above two relation we can solve for m.

One root will be \frac{1}{4} and the others we will get by applying Sridhar Acharya Formula, which will give a pair of conjugate imaginary roots of the equation.  (Answer)

8 0
3 years ago
How do I do this ixl
svetlana [45]
The anwser that I know of is 6x+2
8 0
3 years ago
Factoring Quadratic Expressions:<br> 5p^2 - p - 18
Dennis_Churaev [7]
5 p^{2} -p-18

5 p^{2}-10p+9p-18

5p(p-2)+9(p-2)

(p-2)(5p+9)
3 0
2 years ago
These map tests give me anxiety or however you spell it
Vesnalui [34]

Answer:

Im sorry i dont know what im supposed to be answering

step-by-step explanation:

5 0
3 years ago
Other questions:
  • Sharlene bought 4 CDs at the music store. Each cost 14.95. She was charged 5% sales tax on her purchase. What was the total cost
    8·1 answer
  • I have $2.40 consisting of nickels and dimes. If I have 30 coins how many of each do I have
    14·1 answer
  • The level of a lake was 8 inches below
    8·1 answer
  • Pls someone pls help me with this question pls
    11·1 answer
  • HEB has dish soap that costs $2.80 for a 12oz bottle. Fiesta has the same dish soap that costs $2.00 for a 8 oz tube.
    8·1 answer
  • You borrow $1600 to buy a living room set. The simple interest rate is 9%. You pay off the loan after 3 years. How much do you p
    6·1 answer
  • If there are 574 cals in 160 grams,<br> how many are there in 100 grams
    5·1 answer
  • Which expression is equivalent to 6 (3x + 4)?
    9·2 answers
  • What is 3-4 pls pls pls
    7·1 answer
  • The nearest hundred to 83,752,245 is?
    7·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!