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

Advocard [28]

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

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

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

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

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

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

5 0

3 years ago

Solve for the Simplest form

tino4ka555 [31]

How to solve:

$\frac{5}{6}$ - $\frac{3}{8}$

Write all numerators above the least common denominator which is 24 in this case.
$\frac{20-9}{24}$

Subtract the numbers
$\frac{11}{24}$

Alternate form: 0.458333

The final, simplified, fraction answer is: $\frac{11}{24}$

7 0

3 years ago

Read 2 more answers

Nina owns a vacation home valued at $75,500. She owes $32,126 on her mortgage. How much are the asset and liability values for N

alexandr402 [8]

The value of Nina's house is $75,500. However, she owes $32,126 on her mortgage.
The asset on her house is $75,500
The liability on her house is $32,156
The net worth of the house is $43,344 (difference between assets and liabilities)

5 0

3 years ago

Use properties of addition and subtraction to evaluate the expression. −24−8−26 Enter your answer in the comments below.

Sav [38]

The answer to this would be -58

6 0

3 years ago

Ellen claims she has a coin that is weighted so that the probability of heads is 70%.

kvasek [131]

Outcome Heads Tails
Relative Frequency 0.69 0.31

so first statement is false as 69% is close to 70%.

second statement is false as heads probability is close to 70%

last 2 statements are true:

The theoretical probability of tails is most likely 30%.

It is likely that the coin is not fair.

5 0

3 years ago

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