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Norma-Jean [14]
2 years ago
13

Una poblacion es atacada por una epidemia de gripe sea N(t)= numero de personas enfermas al tiempo t. En dias la epidemia inicio

en N(0)= 50. Un matematico determina que la gripe se extiende a razón de f'(t)= 120t- 3t^2 personas por día. Determina
a) La función original que describe el comportamiento de la epidemia. (Aplica los mismos pasos explicados anteriormente.




b) ¿Cuántos enfermos habrán después de 15 días si no se controla la epidemia?
​
Mathematics
1 answer:
Lisa [10]2 years ago
8 0

Answer:

<em>Habrán 10175 enfermos a los 15 dias.</em>

Step-by-step explanation:

La tasa de cambio de la población enferma por la epidemia de gripe es:

N'(t)=120t-3t^2

Donde t es el tiempo en dias, y se sabe que la epidemia inició en N(0)=50.

a)

Para encontrar la función original que describe el comportamiento de la epidemia, debemos integrar la función:

N(t)=\int N'(t)dt

N(t)=\int (120t-3t^2)dt

Integrando:

\displaystyle N(t)=120\frac{t^2}{2}-3\frac{t^3}{3}+C

Simplificando:

\displaystyle N(t)=60t^2-t^3+C

Para determinar el valor de C, usamos la condición inicial N(0)=50:

\displaystyle 50=60(0)^2-(0)^3+C

Se tiene que C=50, y la función queda determinada como:

\displaystyle N(t)=60t^2-t^3+50

b) El número de enfermos a los t=15 dias se determina substituyendo el valor en la función original:

\displaystyle N(15)=60(15)^2-(15)^3+50

Calculando:

N(15)=13500-3375+50=10175

Habrán 10175 enfermos a los 15 dias.

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