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
Diano4ka-milaya [45]
2 years ago
12

HELP 100 POINTS The population of a city is modeled with the function P=250,000e^0.013t​, where t is the number of years since 2

000. In what year will the population reach ​450,000?
Mathematics
1 answer:
erma4kov [3.2K]2 years ago
6 0
Pretty difficult problem, but that’s why I’m here.
First we need to identify what we’re looking for, which is t. So now plug 450k into equation and solve for t.
450000 = 250000e^0.013t
Now to solve this, we need to remember this rule: if you take natural log of e you can remove x from exponent. And natural log of e is 1.
Basically ln(e^x) = xln(e) = 1*x
So knowing this first we need to isolate e
450000/250000 = e^0.013t
1.8 = e^0.013t
Now take natural log of both
Ln(1.8) = ln(e^0.013t)
Ln(1.8) = 0.013t*ln(e)
Ln(1.8) = 0.013t * 1
Now solve for t
Ln(1.8)/0.013 = t
T= 45.21435 years
Now just to check our work plug that into original equation which we get:
449999.94 which is basically 500k (just with an error caused by lack of decimals)
So our final solution will be in the 45th year after about 2 and a half months it will reach 450k people.
You might be interested in
La la laaaaa don't answer just for the points -_-
Amiraneli [1.4K]

Answer:

\sf C=21.99~ft.

__________

\sf Steps

  • \sf Given~the~diameter~is~7~ft...
  • \sf We~know~we~must~use~diameter-to-circumference~formula

         \sf Formula:  \pi d = \pi  * (diameter) = [Circumference]

__________

\sf Solve

\pi * 7 = 21.99~ft.

6 0
2 years ago
Read 2 more answers
Help can someone help me find value of X ♡ I would appreciate it ;) ​
kotykmax [81]

Answer:

4x°+16°=7x° – 20°

16°+20°=7x°+4x°

36°=11x°

36/11=x°

X°= 3.27272727

4 0
2 years ago
Read 2 more answers
Anyone? Help pweeez :)
Amanda [17]

So one miles for A and the fee is $170 then B is $160 then if you used company A you'd go 3 miles to match company B which their miles would be 2,

which I guess the answer would be 5 miles?

8 0
3 years ago
Yesterday morning, at 6:00 AM, water started leaking from a tank at a constant rate. The tank contained8,496liters of water at 6
GREYUIT [131]

A linear equation can be written as:

y = a*x + b

where a is the slope and b is the y-intercept.

If we know that the line passes through the points (x₁, y₁) and (x₂, y₂) the slope is:

a = \frac{y_2 - y_1}{x_2 - x_1}

The answers are:

a) y = (-12 L/min)*t + 9,000 L

b) 6,840 L

a) Here we know that we can model this situation with a linear equation, we know that the leak starts at 6:00 am, then we define t = 0 as 6:00 am

We know that at 6:42 am  (at t = 42 mins) the tank has 8,496 liters.

And at 7:15 am (at t = 75 mins) the tank has 8,100 liters.

Then we have two points of the line:

(42 mins, 8,496 liters)

(75 mins, 8,100 liters)

Then the slope is:

a = \frac{8,100 liters - 8,496 liters }{75 mins -42 mins } = -12 L/min

So the line will be something like:

y = (-12 L/min)*t + b

To find the value of b, which is the initial volume of water in the tank, we use the point (75 mins, 8,100 liters)

This means that if t = 75 mins, then we have y = 8,100 L

So we can replace these two on the above equation:

8,100 L = (-12 L/min)*75 mins + b

8,100L = -900L + b

8,100L + 900L = b = 9,000 L

Then the linear equation is:

y = (-12 L/min)*t + 9,000 L

b) Now we want to know how much water is in the tank at 9:00 am.

Notice that 9:00 am is 3 hours after 6:00 am, our t = 0.

Then  9:00am is equivalent to t = 180 mins.

So to know the volume of water that there is in the tank at 9:00 am, we just need to evaluate the linear function at t = 180 mins.

y = (-12 L/min)*180 mins + 9,000 L = 6,840 L

If you want to learn more, you can read:

brainly.com/question/24594539

7 0
2 years ago
Write the equation of the circle with center (−3, −2) and (4, 5) a point on the circle.
SSSSS [86.1K]
Your answer should be B
5 0
3 years ago
Read 2 more answers
Other questions:
  • 50% of all the cakes jenny baked were party cakes, 1/5 were fruit cakes and the remainder were sponge cakes. What percentage of
    11·1 answer
  • If two pounds of peaches are 4.20 how much is five pounds
    6·2 answers
  • PLEASE HELP!!!!!!!!!!
    11·2 answers
  • if five times a number added to 4 is divided by the number plus 6 the result is nine halves, Find The Number
    10·1 answer
  • Jerry has two same size circles divided into same number of equal parts. One circle has has 3/4 of the parts shaded and the othe
    11·1 answer
  • Casey is going to start selling ice cream cones at the county fait. He has to rent the equipment for $26 and spend $0.43 on ingr
    12·2 answers
  • Find the volume of a scented candle that is in the shape of a cylinder with a diameter of 16 centimeters and a height of 20 cent
    5·2 answers
  • Find the values of x when y=1
    11·1 answer
  • Marsha is driving 630 otal miles on a trip. She has already driven 2/5 of the distance. How far has Marsha driven?
    9·1 answer
  • In F,if BF = 6 cm, then FD= __cm.
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!