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Dafna1 [17]
3 years ago
10

The population of a county is growing at a rate of 9% per year, compounded continuously. How many years will it take for the pop

ulation to quadruple according to the exponential growth function? Round your answer up to the nearest whole number, and do not include units.
Mathematics
1 answer:
Liula [17]3 years ago
6 0

It will take 15 years for the population to quadruple

Step-by-step explanation:

The formula for continuously compounding rate is  A=Pe^{rt} , where

  • A is the future amount
  • P is the initial amount
  • r is the interest as a decimal
  • t is the time in years

Assume that the initial population is P

∵ The initial population = P

∵ The growth rate = 9% ⇒ compounded continuously

∴ r = \frac{9}{100} = 0.09

∵ The population will quadruple in t years

∴ A = 4P

- Substitute these values in the formula

∵ A=Pe^{rt}

∴ 4P=Pe^{(0.09)t}

- Divide both sides by P

∴ 4=e^{0.09t}

- Insert ㏑ to both sides

∴ ㏑(4) = ㏑( e^{0.09t} )

∵ ㏑( e^{n} ) = n

∴ ㏑ (4) = 0.09 t

- Divide both sides by 0.09

∴ t = 15.4

∴ t = 15 years to the nearest whole number

It will take 15 years for the population to quadruple

Learn more:

You can learn more about the logarithmic function in brainly.com/question/11921476

#LearnwithBrainly

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zhannawk [14.2K]

Answer: $166.430 per year

Step-by-step explanation:

0= -900000+AOC(P/A, 40%,3)

0= -900000+AOC(1.5889)

result we get

AOC= $566430

Require reduction = 566430-400000

result we get

$166.430 per year

8 0
3 years ago
Please provide all steps given to find the answer. Thanks!!!<br> Simplify: 5(2x+9)²
gulaghasi [49]

Answer:

20x²+180x + 405

Step-by-step explanation:

Follow PEMDAS to know what you do first

square (2x + 9) by foiling

(2x+9) (2x + 9)

= 4x²+ 36x + 81

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20x²+180x + 405

4 0
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What is the scale factor from Figure A to Figure B?
JulijaS [17]

Answer:

  • 1/3

Step-by-step explanation:

The figure B is the scaled copy of the figure A.

The both figures are similar to each other.

<u>The scale factor is the ratio of corresponding sides of figure B to A:</u>

  • k = 3/9 = 1/3

or

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5 0
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MakcuM [25]
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PLEASE HELP ASAP!! WILL GIVE BRAINIEST + 30 POINTS!!
Goryan [66]

Given rectangle RUTS, the missing reasons that justifies the five statements in the two-column proof are:

  1. Given
  2. Definition of rectangle.
  3. Definition of rectangle.
  4. By SAS Congruence Theorem.
  5. By CPCTC.

<h3>What is a Rectangle?</h3>
  • A rectangle is a quadrilateral.
  • All four angles in a rectangle are right angles.
  • The opposite sides of a rectangle are parallel and congruent to each other.

Therefore, based on what we are given and the definition of a rectangle, we can establish that △URS ≅ △STU by SAS.

Since △URS ≅ △STU, therefore ∠USR = ∠SUT by CPCTC.

In conclusion, given rectangle RUTS, the missing reasons that justifies the five statements in the two-column proof are:

  1. Given
  2. Definition of rectangle.
  3. Definition of rectangle.
  4. By SAS Congruence Theorem.
  5. By CPCTC.

Learn more about properties of rectangle on:

brainly.com/question/2835318

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