MATHEMATICS COLLEGE

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:

Answers

Answer 1
Answer:

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

P(0) = 0 and P(50) = 1,500,000

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

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

The integrating factor 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((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)=(1)/(2)\Rightarrow K=-(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)

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Answers

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Solve for x x-23=17 NEED TO KNOW FAST PLEASE!!!!

Answers

Answer:

x = 40

Step-by-step explanation:

Adding 23 to both sides gives us:

x - 23 + 23 = 17 + 23

x = 40

Answer:

\boxed{ \bold{ \bold{ \sf{x = 40}}}}

Step-by-step explanation:

\sf{x - 23 = 17}

Move constant to right hand side and change it's sign

\sf{x = 17 + 23}

Add the numbers

\sf{x = 40}

Hope I helped!

Best regards!!

11 m 40 cm + 58 m 30 cm

Answers

Answer:

69 m 70 cm

Step-by-step explanation:

Caroline needed to get her computer fixed. She took it to the repair store. The technician at the store worked on the computer for 2.75 hours and charged her $114 for parts. The total was $320.25. Write and solve an equation which can be used to determine xx, the cost of the labor per hour.​

Answers

2.75(x)+114=320.25
-114 -114
2.75(x)=206.25
/2.75. /2.75
X=75

It costs 75$ per hour


This is because we don’t know how much they charge per hour but we know the number of hours spend working on the computer, so you have to do 2.75(x) where x represents the cost per hour And we also know that the cost of the part is $114 so we have to add that to
(2.75(x)+114) the equation then finally you have to make the expression equal to 320.25 since we know the final cost so

2.75(x)+114=320.25

Final answer:

The equation to solve this problem is 114 + 2.75x = 320.25. Solving this equation, we find that the cost of labor per hour, represented by x, is $75.

Explanation:

The problem you're trying to solve involves the labor cost per hour of the technician who worked on Caroline's computer. From the problem, we know that the total cost of the repair was $320.25. This includes the cost of parts, which was $114, and the labor the technician invested, which we know took 2.75 hours but we aren't sure of the per hour cost. Let's denote this unknown cost as x. Therefore, our equation would be 114 + 2.75x = 320.25.

We can solve for x, the cost of labor per hour, by isolating this variable on one side of the equation. Firstly, subtract 114 from both sides: 2.75x = 320.25 - 114 which results in 2.75x = 206.25. Then, divide both sides by 2.75 to find x: x = 206.25/2.75 which equals $75. Therefore, the cost of labor per hour is $75.

Learn more about Labor Cost here:

brainly.com/question/30801165

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