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2 years ago

Find the 14th term of the geometric sequence 5 -10 20

Mathematics

2 answers:

Anna [14]2 years ago

7 0

Answer:

a14 = -40,960

Step-by-step explanation:

The sequence has a first term of 5 and a common ratio of -10/5 = -2, so the n-th term is given by ...

an = a1·r^(n-1)

an = 5·(-2)^(n-1)

The 14th term is then ...

a14 = 5·(-2)^(14-1) = -5·2^13 = -5·8192

a14 = -40,960

bulgar [2K]2 years ago

5 0

Well since the person above me explained it already it’s that answer

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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

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

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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

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

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

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

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2 years ago

Which number line models the solution set of -2x + 7 > 17?Pls do 2 answers for good measures (and brainliest)

Sidana [21]

Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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