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
Zolol [24]
3 years ago
8

An advertising company designs a campaign to introduce a new product to a metropolitan area of population 3 Million people. Let

P(t) denote the number of people (in millions) who become aware of the product by time t. Suppose that P increases at a rate proportional to the number of people still unaware of the product. The company determines that no one was aware of the product at the beginning of the campaign, and that 50% of the people were aware of the product after 50 days of advertising. The number of people who become aware of the product at time t is:
Mathematics
1 answer:
Advocard [28]3 years ago
5 0

Answer:

P(t)=3,000,000-3,000,000e^{0.0138t}

Step-by-step explanation:

Since P(t) increases at a rate proportional to the number of people still unaware of the product, we have

P'(t)=K(3,000,000-P(t))

Since no one was aware of the product at the beginning of the campaign and 50% of the people were aware of the product after 50 days of advertising

<em>P(0) = 0 and P(50) = 1,500,000 </em>

We have and ordinary differential equation of first order that we can write

P'(t)+KP(t)= 3,000,000K

The <em>integrating factor </em>is

e^{Kt}

Multiplying both sides of the equation by the integrating factor

e^{Kt}P'(t)+e^{Kt}KP(t)= e^{Kt}3,000,000*K

Hence

(e^{Kt}P(t))'=3,000,000Ke^{Kt}

Integrating both sides

e^{Kt}P(t)=3,000,000K \int e^{Kt}dt +C

e^{Kt}P(t)=3,000,000K(\frac{e^{Kt}}{K})+C

P(t)=3,000,000+Ce^{-Kt}

But P(0) = 0, so C = -3,000,000

and P(50) = 1,500,000

so

e^{-50K}=\frac{1}{2}\Rightarrow K=-\frac{log(0.5)}{50}=0.0138

And the equation that models the number of people (in millions) who become aware of the product by time t is

P(t)=3,000,000-3,000,000e^{0.0138t}

You might be interested in
Which of the following shows a circle circumscribed about a triangle?
Dima020 [189]

Answer: The first option.

Step-by-step explanation:

1. By definition,  when a circle circumscribed about a triangle it passes through all the vertices of that triangle (As you know, a triangle has three vertices).

2. As you can see in the figure attached, the only circle that passes through three vertices of the triangle is the the circle of the first optin. Therefore, you can conclude that that circle is circumscribed about the triangle.

5 0
3 years ago
Quick!!
Ira Lisetskai [31]

Answer:

c) three

-----------------------------------------------------------------------------------------------------------------

Step-by-step:

The tetrahedron is a triangular pyramid with equilateral triangles on each face.

3 0
2 years ago
Read 2 more answers
The cost price of a jacket is 600. It was sold with a profit of 5%. Find the
pickupchik [31]

570

600×0.95 = 570

I did this because if they made a 5% profit them you substrate that from 100 and divide the original price from what you get.

4 0
2 years ago
Read 2 more answers
If 5²+m × 5⁷ =5¹⁵ ,find the value of m<br>please answer this question fast thank you!​
rewona [7]

Answer:

m = 6

Step-by-step explanation:

Here, we want to find the value of m

To do this, we use the indices addition property for multiplication

On the left hand side;

5^(2 + m + 7) = 5^15

5^(m + 9) = 5^15

since the bases are equal, we equate the powers

m + 9 = 15

m = 15-9

m = 6

4 0
3 years ago
Help!!!!!!!!!!!!!!!!!!!
PilotLPTM [1.2K]
The answer to your question is A
6 0
3 years ago
Other questions:
  • Two angels of a triangle measure 65 and 75. Which is not the measure of an exterior angle of the triangle
    13·1 answer
  • X^3-13x^2+40x=0 quadratic
    12·1 answer
  • 10×4ones= ____ones=
    15·1 answer
  • Solve the following system of equations graphically.
    12·1 answer
  • 6. Solve the following equation for x. Show each step.<br> 5x + 2 = 3x + 4(2x - 1)
    13·2 answers
  • Six years ago my son was one-third my age at that time.
    14·1 answer
  • The question is on the photo
    5·2 answers
  • What is the slope of a line parallel to y=1/3x + 2 explain.
    5·1 answer
  • PLEASE SOLVE AND CHECK. SHOW COMPLETE SOLUTION
    15·1 answer
  • HELP PLS Match each graph with the logarithmic function it represents
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!