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
bearhunter [10]
3 years ago
6

A village experienced 2% population growth, compounded continuously, each year for 10 years. At the end of the 10 years, the pop

ulation was 158.
1. What was the population of the village at the beginning of the 10 years according to the exponential growth function? Round your answer up to the next whole number, and do not include units.
Mathematics
2 answers:
pantera1 [17]3 years ago
6 0

Answer:

The initial population at the beginning of the 10 years was 129.

Step-by-step explanation:

The population of the village may be modeled by the following function.

P(t) = P_{0}e^{rt}

In which P is the population after t hours, P_{0} is the initial population and r is the growth rate, in decimal.

In this problem, we have that:

P(10) = 158, r = 0.02.

So

158 = P_{0}e^{0.02*10}

P_{0} = 158*e^{-0.2}

P_{0} = 129

The initial population at the beginning of the 10 years was 129.

EastWind [94]3 years ago
4 0

Answer:

Step-by-step explanation:

The formula representing the population growth after t years can be expressed as

A = P(1+r/n)^nt

Where

A is the population of the village after t years.

P represents the initial population of the village at the beginning of the 10 years.

r represents population growth rate

n represents the number of times that the population was compounded in each year.

From the given information,

A = 158

r = 2% = 2/100 = 0.02

t = 10 years

n = 1 because it was compounded continuously each year.

Therefore

158 = P(1+0.02/1)^1×10

158 = P(1.02)^10

P = 158/(1.02)^10 = 129.615

Approximately 130 to the nearest whole number.

You might be interested in
What is the measure of an angle that turns through 3/4 of a complete circle
ANEK [815]
270 degrees this because when you count each angle it is 90 degrees then 180 degrees then 270 
4 0
3 years ago
Read 2 more answers
I'm stuck! help! please? ​
Alchen [17]

Answer:

x = 2

Step-by-step explanation:

2 to the second power is 4. 4 subtracted by 4 is zero.

7 0
3 years ago
A rectangular window is topped with a semicircle the height of the rectangle part is 1 more than 3 times its width W meters whic
devlian [24]

Answer:

A = 3W² + W + 1/8πW²

Step-by-step explanation:

rectangular window is L x W

semicircle is 1/2 πr²

r = 1/2 W

L = 3W + 1

A = W(3W + 1) + 1/2 π(1/2W)²

A = 3W² + W + 1/8πW²

4 0
3 years ago
Read 2 more answers
What is the solution of
kobusy [5.1K]

Answer:

Third option: x=0 and x=16

Step-by-step explanation:

\sqrt{2x+4}-\sqrt{x}=2

Isolating √(2x+4): Addind √x both sides of the equation:

\sqrt{2x+4}-\sqrt{x}+\sqrt{x}=2+\sqrt{x}\\ \sqrt{2x+4}=2+\sqrt{x}

Squaring both sides of the equation:

(\sqrt{2x+4})^{2}=(2+\sqrt{x})^{2}

Simplifying on the left side, and applying on the right side the formula:

(a+b)^{2}=a^{2}+2ab+b^{2}; a=2, b=\sqrt{x}

2x+4=(2)^{2}+2(2)(\sqrt{x})+(\sqrt{x})^{2}\\ 2x+4=4+4\sqrt{x}+x

Isolating the term with √x on the right side of the equation: Subtracting 4 and x from both sides of the equation:

2x+4-4-x=4+4\sqrt{x}+x-4-x\\ x=4\sqrt{x}

Squaring both sides of the equation:

(x)^{2}=(4\sqrt{x})^{2}\\ x^{2}=(4)^{2}(\sqrt{x})^{2}\\ x^{2}=16 x

This is a quadratic equation. Equaling to zero: Subtract 16x from both sides of the equation:

x^{2}-16x=16x-16x\\ x^{2}-16x=0

Factoring: Common factor x:

x (x-16)=0

Two solutions:

1) x=0

2) x-16=0

Solving for x: Adding 16 both sides of the equation:

x-16+16=0+16

x=16

Let's prove the solutions in the orignal equation:

1) x=0:

\sqrt{2x+4}-\sqrt{x}=2\\ \sqrt{2(0)+4}-\sqrt{0}=2\\ \sqrt{0+4}-0=2\\ \sqrt{4}=2\\ 2=2

x=0 is a solution


2) x=16

\sqrt{2x+4}-\sqrt{x}=2\\ \sqrt{2(16)+4}-\sqrt{16}=2\\ \sqrt{32+4}-4=2\\ \sqrt{36}-4=2\\ 6-4=2\\ 2=2

x=16 is a solution


Then the solutions are x=0 and x=16


5 0
3 years ago
Maria is renting kayaks from a local shop that charges a $10 fee, plus an hourly rate of $7.50.
omeli [17]

Answer:

8 hours

Step-by-step explanation:

70-10

60÷7.50= 8 hours

3 0
3 years ago
Other questions:
  • PLEASE HELP MATH QUESTION !!! Explain!
    8·1 answer
  • Please someone factor 8 + 16 !!!!!
    7·1 answer
  • What is the value of x? x = 23   x = 35 x = 58 x = 93
    10·2 answers
  • Heyy please help with this question - i'll give brainliest :))
    5·2 answers
  • Garrett buys lunch for himself and his friend. He buys 2 sandwiches, 2 fries, and 2 malts. How much did Garrett spend on lunch?
    9·1 answer
  • Which statement is true about comparing 5.37 and 5.4?
    7·1 answer
  • PLEASE HELP NEED ASAP!
    8·1 answer
  • Help me with this pls
    11·2 answers
  • Which of the following represents the graph of the function f(x)=log3X+2
    13·1 answer
  • Write an integral in polar coordinates equivalent to the following:​
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!