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
gizmo_the_mogwai [7]
2 years ago
11

The population of a community is known to increase at a rate proportional to the number of people present at time t. The initial

population P0 has doubled in 5 years. Suppose it is known that the population is 12,000 after 3 years. What was the initial population P0?
Mathematics
1 answer:
GREYUIT [131]2 years ago
4 0

Answer:

P(0) = 7,917

Step-by-step explanation:

The population of the community is given by the following formula:

P(t) = P(0)(1+r)^{t}

In which P(0) is the initial population and r is the growth rate.

The initial population P0 has doubled in 5 years.

This means that

P(5) = 2P(0)

Which lets us find r.

P(t) = P(0)(1+r)^{t}

2P(0) = P(0)(1+r)^{5}

(1+r)^{5} = 2

Applying the 5th root to both sides

1+r = 1.1487

r = 0.1487

So

P(t) = P(0)(1.1487)^{t}

Suppose it is known that the population is 12,000 after 3 years.

With this, we find P(0)

P(t) = P(0)(1.1487)^{t}

12000 = P(0)(1.1487)^{3}

1.5157P(0) = 12000

P(0) = \frac{12000}{1.5157}

P(0) = 7917

You might be interested in
What is the value of the digit 6 in the number 5263148
Karolina [17]
60,000 so tenthousands
4 0
3 years ago
What is 32.15 in unit form??
tekilochka [14]
3 tens, 2 ones, 1 tenth, 5 hundredths
4 0
3 years ago
Read 2 more answers
A person gets on and off a bathroom scale four times. The four readings (in pounds) are 148, 151, 150, and 152. Each time after
Ganezh [65]

Answer:

See explanation below

Step-by-step explanation:

Since each time after the person gets off the scale, the reading is 2 lb the person's weight must be near the mean of

148-2, 151-2, 150-2, 152-2; that is to say, near the mean of 146, 149, 148, 150 = (146+149+148+150)/4 = 148.25

We could estimate the uncertainty as <em>the standard error SE </em>

\bf SE=\frac{s}{\sqrt{n}}  

where  

<em>s = standard deviation of the sample </em>

<em>n = 4 sample size. </em>

Computing s:

\bf s=\sqrt{\frac{(146-148.25)^2+(149-148.25)^2+(148-148.25)^2+(150-148.25)^2}{4}}=1.479

So, the uncertainty is 1.479/2 = 0.736

<em>It is not possible to estimate the bias, since it is the difference between the true weight and the mean, but we do not know the true weight. </em>

5 0
2 years ago
3. What are the intersection points of the line whose equation is y=3x +3 and the
densk [106]

Answer:

Points of intersection of these graphs are (-2, -3) and (0.6, 4.8).

Step-by-step explanation:

Equation of the circle → (x - 2)² + y² = 25 ---------(1)

                                   → (x - 2)² + (y - 0)² = 5²

By comparing this equation with the standard equation of the circle,

(x - a)² + (y - b)²= r²

Here (a, b) is the center and r is the radius of the circle.

Therefore, center of the circle is (2, 0) and radius = 5 units

Second equation is a linear equation → y = 3x + 3 -------(2)

x-intercept of the equation → x = -1

y-intercept of the equation → y = 3

By graphing these equations we can get the point of intersections.

Solving these equations algebraically,

Substitute the value of y from equation (2) in the equation (1),

(x - 2)² + (3x + 3)² = 25

x² - 4x + 4 + 9x² + 18x + 9 = 25

10x² + 14x - 12 = 0

5x² + 7x - 6 = 0

x = \frac{-7\pm \sqrt{7^2-4(5)(-6)}}{2(5)}

x = \frac{-7\pm \sqrt{169}}{10}

x = \frac{-7\pm13}{10}

x = -2, 0.6

From equation (2),

y = -3, 4.8

Therefore, points of intersection of these graphs are (-2, -3) and (0.6, 4.8).

6 0
3 years ago
Find the area of the figure.<br> A-56cm^2<br> B-88cm^2<br> C-112cm^2<br> D-384cm^2
julia-pushkina [17]
  • firstly find the area of the square which is sidexside=8x8=64cm^2
  • then find the area of the triangle which is 1/2xbasexhight=1/2x8x6=24cm^2
  • THEN add both areas (64+24)=88cm^2

4 0
2 years ago
Other questions:
  • Solve the equation.
    10·1 answer
  • What does 590x89 equals ??
    8·1 answer
  • Please what is the answer?
    15·1 answer
  • Ross resides in an apartment where houses are arranged horizontally. She resides at door number 3.if she want to visit her frien
    13·1 answer
  • Find the value of x please!!! Rlly important!
    15·2 answers
  • What word is the same flipped backwards , forwards and had 4 letters?
    5·2 answers
  • What is the first step when examining a data set? *
    7·1 answer
  • Plz help i really need this answer don't do it for the points please. A student receives a gift card to an ice cream shop. The g
    15·1 answer
  • Please Help! Will Mark Brainliest!
    5·2 answers
  • A baker baked 8 060 loaves of bread in January. If he baked the same number of loaves of bread everyday, how many loaves of brea
    13·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!