thanks to its environmental initiatives, hampton has cut its annual co2 emissions by 14%. this year, the…

thanks to its environmental initiatives, hampton has cut its annual co2 emissions by 14%. this year, the town produced 87,280 metric tons of emissions. if the downward trend continues, how much co2 will be produced 11 years from now? if necessary, round your answer to the nearest whole number. metric tons

thanks to its environmental initiatives, hampton has cut its annual co2 emissions by 14%. this year, the town produced 87,280 metric tons of emissions. if the downward trend continues, how much co2 will be produced 11 years from now? if necessary, round your answer to the nearest whole number. metric tons

Answer

Explanation:

Step1: Identificar la fórmula de decrecimiento exponencial

La fórmula para el decrecimiento exponencial es $A = P(1 - r)^t$, donde $A$ es la cantidad final, $P$ es la cantidad inicial, $r$ es la tasa de decrecimiento (en decimal) y $t$ es el tiempo. Aquí, $P = 87280$, $r=0.14$ y $t = 11$.

Step2: Sustituir valores en la fórmula

$A=87280\times(1 - 0.14)^{11}$. Primero, calculamos $1-0.14 = 0.86$. Entonces, $A = 87280\times(0.86)^{11}$.

Step3: Calcular $(0.86)^{11}$

$(0.86)^{11}\approx0.1637$.

Step4: Calcular el valor final de $A$

$A = 87280\times0.1637\approx14288$.

Answer:

14288