Question

a small country emits 115,000 kilotons of carbon dioxide per year. in a recent global agreement, the country agreed to cut its carbon emissions by 1.6% per year for the next 11 years. in the first year of the agreement, the country will keep its emissions at 115,000 kilotons and the emissions will decrease 1.6% in each successive year. how many total kilotons of carbon dioxide would the country emit over the course of the 11 - year period, to the nearest whole number? answer attempt 1 out of 2

Explanation:

Step1: Identify the type of sequence

This is a geometric - series problem. The first term $a = 115000$, and the common ratio $r=1 - 0.016=0.984$. The number of terms $n = 11$.

Step2: Use the sum formula for a geometric series

The sum formula for a geometric series is $S_n=\frac{a(1 - r^n)}{1 - r}$ when $r
eq1$.
Substitute $a = 115000$, $r = 0.984$, and $n = 11$ into the formula:
$S_{11}=\frac{115000\times(1 - 0.984^{11})}{1 - 0.984}$

Step3: Calculate $0.984^{11}$

$0.984^{11}\approx0.83379$

Step4: Calculate the numerator

$1-0.984^{11}=1 - 0.83379 = 0.16621$
$115000\times(1 - 0.984^{11})=115000\times0.16621 = 19114.15$

Step5: Calculate the denominator

$1 - 0.984=0.016$

Step6: Calculate the sum

$S_{11}=\frac{19114.15}{0.016}=1194634.375\approx1194634$

Answer:

$1194634$