A city currently has 31,000 residents and is adding new residents steadily at the rate of 1200 per year. If the proportion of residents that remain after t years is given by S(t) = 1/(t + 1), what is the population of the city 7 years from now?

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Answer 1
Answer:

Answer:

Population of the city after 7 years from now, P(7) = 6370

Given:

Initial Population, P_(i) = 31000

rate, r(t) = 1200 /yr

S(t) = [/tex]\frac{1}{1 + t}[/tex]

Step-by-step explanation:

Let the initial population be  P_(i) = 31000

The population after T years is given by the equation:

P(T) = P_(i)S(T) + \int_(0)^(T)S(T - t)r(t) dt          (1)

Thus, the population after 7 years from now is given by using eqn (1):

P(7) = (3100)/(1 + 7) + 1200\int_(0)^(7)(1)/(8 - t) dt

P(7) = 3875 - 1200ln(8 - t)|_(0)^(7)

P(7) = 3875 - 1200ln(8 - t)|_(0)^(7)

P(7) = 3875 - 1200(ln(1) - ln(8))

P(7) = 3875 + 2495 = 6370


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Considere as mesas com 4 cadeiras, com 6 cadeiras e com 8 cadeiras. ©Shutterstock/jenjira Com base nessa sequência de imagens, qual expressão indica a quantidade de cadeiras utilizadas ao colocarmos n mesas lado a lado?

Answers

Responder:

C. Tₙ = 2n + 2

Explicación paso a paso:

De la pregunta, la secuencia de imágenes, cuya expresión indica es 4 cadeiras, 6 cadeiras, 8 cadeiras ...

Se puede ver la secuencia una progresión aritmética de la forma 4, 6, 8 ... Para obtener la expresión que indica la cantidad de cadenas utilizadas o colocaremos n tablas una al lado de la otra, tendremos que encontrar el enésimo término de la secuencia que usa la fórmula para encontrar el enésimo término de una secuencia aritmética.

El enésimo término de un AP se expresa como Tₙ = a + (n-1) d donde;

a es el primer término

n es el número de términos es la diferencia común

De la secuencia generada, a = 4, d = 6-4 = 8-6 = 2

Tₙ = 4+ (n-1) 2

abre el paréntesis

Tₙ = 4 + 2n-2

Tₙ = 2n + 4-2

Tₙ = 2n + 2

Por lo tanto, la expresión que indica la cantidad de cadenas utilizadas o colocaremos n tablas una al lado de la otra es 2n + 2

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