Question

Un departamento de policía sabe que el crecimiento de la ciudad y el número de robos está relacionado por una ecuación lineal. Los registros del municipio muestran que 270 robos se cometieron en un año cuando la población era de 121200 , y que se reportaron 650 robos en un año cuando la población era de 361900 ¿Cuántos robos se espera que ocurran cuando la población llegue a 160800

Answer 1

The number of robberies that are expected to occur when the population reaches 160,800 is 715.

How do we predict the likely number of robberies?

We can use the two data points to find the equation of the line that relates the population and the number of robberies. Let x be the population and y be the number of robberies. Then we have:

Point 1:
`(x1, y1) = (121,200, 270)`

Point 2:
`(x2, y2) = (361,900, 650)`

The slope of the line can be found using the formula: slope = (y2 - y1) / (x2 - x1)

Substituting the values we get:

`= (650 - 270) / (361900 - 121200)\\= 380 / 240700\\= 0.0015787287\\= 0.001579`

The equation of the line can be written in the form:

y - y1 = m(x - x1)

Substituting the values of point 1 and the slope we get:

`y - 270 = 0.001579(x - 121200)\\y - 270 = 0.001579x - 191.3748\\y = 0.001579x - 461.3748`

Now we can substitute the population of 160,800 to find the expected number of robberies:

`y = 0.001579(160800) - 461.3748\\y = 253.9032 + 461.3748\\y = 715.278\\y = 715`

Therefore, we can expect about 715 robberies to occur when the population reaches 160,800.

Translated question "A police department knows that the growth of the city and the number of robberies are related by a linear equation. Township records show that 270 robberies were committed in a year when the population was 121,200, and that 650 robberies were reported in a year when the population was 361,900. How many robberies are expected to occur when the population reaches 160,800?"

equation