Question

2 the table below shows the concentration of ozone in earths atmosphere at different altitudes. write the exponential regression equation that models these data, rounding off values to the nearest thousandth. concentration of ozone altitude (x) ozone units (y) 0 0.7 5 0.6 10 1.1 15 3.0 20 4.9 d) write an exponential regression equation using desmos. round to the second place value. y = ( )^x e) according to the model, what percent is the ozone unit increasing by as the altitude increases? ____% f) using your model, predict what the ozone unit will be if the altitude is at 30

Explanation:

Step1: Obtener ecuación de regresión

Usamos los datos $(x,y)$: $(0,0.7)$, $(5,0.6)$, $(10,1.1)$, $(15,3.0)$, $(20,4.9)$ en Desmos para calcular la regresión exponencial de la forma $y = ab^x$. Los valores redondeados a dos decimales son $a=0.70$ y $b=1.12$.
$$y = 0.70(1.12)^x$$

Step2: Calcular porcentaje de aumento

El factor de crecimiento es $b=1.12$. El porcentaje de aumento se obtiene restando 1 y multiplicando por 100.
$$(1.12 - 1) \times 100 = 12\%$$

Step3: Predecer ozono a 30 km

Sustituimos $x=30$ en la ecuación de regresión.
$$y = 0.70(1.12)^{30}$$
Calculamos $(1.12)^{30} \approx 29.96$, luego:
$$y = 0.70 \times 29.96 \approx 20.97$$

Answer:

D) $y = 0.70(1.12)^x$
E) 12%
F) 21.0 (o 20.97, redondeado a un decimal)