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
irina [24]
3 years ago
9

In 2016 the United States had a population of about 323 million people and was growing at 0.7 %. Use an explicit exponential mod

el to predict what year the U.S. population will reach 400 million people
Mathematics
1 answer:
ElenaW [278]3 years ago
5 0

Answer:

2047

Step-by-step explanation:

We are given that

Growing rate=0.7%

\frac{dp}{dt}=\frac{0.7}{100}P

\int \frac{dP}{P}=0.007\int dt

lnP=0.007t+C

Using the formula

\int \frac{dx}{x}=ln x+C

P=e^{0.007t+C}=e^{0.007t}\cdot e^C=Ae^{0.007t}

e^C=A

Initially when t=0,P=323 million

Substitute the values

323 million=A

P=323e^{0.007t}

Now, substitute P=400 million

400=323e^{0.007t}

ln\frac{400}{323}=0.007t

ln(1.2384)=0.007t

t=\frac{ln(1.2384}{0.007}

t=30.5\approx 31 Years

Year=2016+31=2047

Hence,In 2047 the U.S population will reach 400 million people.

You might be interested in
A man travels 20 km by car from Town P to Town Q at an average speed of x km/h. He finds that the time of the journey would be s
yuradex [85]

Answer:

x = 20.

Step-by-step explanation:

First, you should remember the relation:

Distance = Speed*Time.

First, we know that a man travels a distance of 20km at a speed of x km/h, in a time T.

We can write this as:

20km = (x km/h)*T

We know that the time is shortened by 12 minutes if the speed is increased by 5km/h

Rewriting these 12 minutes in hours (remember that 60min = 1 hour)

12 min = (12/60) hours = 0.2 hours

Then from this, he can travel the same distance of 20km in a time T minus 0.2 hours if the speed is increased by 5 km/h

We can write this as:

20km = (x + 5 km/h)*(T - 0.2 h)

Then we have a system of two equations, and we want to find the value of x:

20km = (x km/h)*T

20km = (x + 5 km/h)*(T - 0.2 h)

First, we should isolate the variable T in one of the equations, if we isolate it in the first one, we will get:

20km/(x km/h) = T

Replacing that in the other equation we get:

20km = (x + 5 km/h)*(T - 0.2 h)

20km = (x + 5 km/h)*( 20km/(x km/h) - 0.2 h)

Now we can solve this for x.

Removing the units (that we know that are correct) so the math is easier to read, we get:

20 = (x + 5)*(20/x - 0.2)

We only want to solve this for x.

20 = x*20/x - x*0.2 + 5*20/x - 5*0.2

20 = 20 - 0.2*x + 100/x - 1

subtracting 20 in both sides we get:

20 - 20 = 20 - 0.2*x + 100/x - 1 - 20

0 = -0.2*x + 100/x - 1

If we multiply both sides by x we get:

0 = -0.2*x^2 + 100 - x

-0.2*x^2 - x + 100 = 0

This is just a quadratic equation, we can solve it using the Bhaskara's equation, the solutions are:

x = \frac{-(-1) \pm \sqrt{(-1)^2 - 4*(-0.2)*100} }{2*-0.2}  = \frac{1 \pm 9 }{-0.4}

Then the two solutions are:

x = (1 + 9)/-0.4 = -25

x = (1 - 9)/-0.4 = 20

As x is used to represent a speed, the negative solution does not make sense, so we should use the positive one.

x = 20

then the average speed initially is 20 km/h

3 0
2 years ago
Find the surface area of the cylinder give your answer in terms of pi. The radius is 4mm and the height is 5mm
Komok [63]
The surface area of a cylinder is the area of the bases plus the area of the side, or SA = 2*A₁ + A₂

Since the area of a circle is \pi r^{2},
SA = 2*(\pi r^{2}) + A₂

Since the area of the side is height * the circumference of the circle or A₂ = h * 2 \pi r, then SA must be;

SA = 2* \pi (r ^{2} )+h*2 \pi r
SA = 2* \pi (4 ^{2} )+5*2 \pi (4)
SA = 32* \pi+80 \pi
SA ≈ <span>351.858377202</span>
3 0
3 years ago
Plz help will be thanked and will pick out brainly
Brums [2.3K]
The answer is 32
Hope this helps:D
have a great rest of a brainly day!
5 0
2 years ago
Three eighths of the students in a class of 32 students are boys. How many students are boys?
nata0808 [166]
12 because 1/8 is 4 4x3= 12
4 0
3 years ago
Read 2 more answers
2 box plots. The number line goes from 60 to 79. For the swim team, the whiskers range from 64 to 74, and the box ranges from 71
mestny [16]

Answer:

2 and 5

Step-by-step explanation:

7 0
3 years ago
Read 2 more answers
Other questions:
  • Eileen’s cookies charges $0.40 per cookie with a delivery fee of $8. Insomnia cookies charges $1.50 per cookie with a $2.50 deli
    11·1 answer
  • If G (x) = 1/x were shifted 2 untold to the left and 2 united up, what would the new equation be?
    12·1 answer
  • A student working on a report about mathematicians decides to find the 98% confidence interval for the difference in mean age at
    12·1 answer
  • What value of x makes this equation true?<br><br> -3x + 10 = 5x + -8
    8·1 answer
  • Please help! Will give branliest for correct answer ! <br> God Bless uu!!
    15·2 answers
  • What is the spread of the data? Please help
    12·1 answer
  • Help me plzzzzzzzzzzzzzzzzz
    7·1 answer
  • A bag is full of green pieces of paper and yellow pieces of paper. A player collects data by drawing pieces of paper from a bag.
    10·1 answer
  • If m ABC = 122°, and m<br> then m
    12·1 answer
  • Please help! I will mark as brainliest IF answer is right. &lt;3
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!