Belmont is a growing industrial town. Every year, the level of CO2 emissions from the town increases by 10%. If the town produced 330,000 metric tons of CO2 this year, how much will be produced 6 years in the future? If necessary, round your answer to the nearest whole number. ____ metric tons

Identify initial CO2 emissions: Identify the initial amount of CO2 emissions and the rate of increase. The initial amount of CO2 emissions is 330,000 metric tons, and the rate of increase is 10% per year.Determine growth formula: Determine the formula for exponential growth. The formula for exponential growth is P(t) = P0 * (1 + r)^t, where P(t) is the amount after time t, P0 is the initial amount, r is the rate of increase, and t is the time in years.Convert rate to decimal: Convert the rate of increase to a decimal. A 10% increase is the same as multiplying by 1.10, so r = 0.10.Substitute values into formula: Substitute the values into the exponential growth formula. P(t) = 330,000 * (1 + 0.10)^6Calculate CO2 emissions after 6 years: Calculate the amount of CO2 emissions after 6 years. P(6) = 330,000 * (1.10)^6 P(6) = 330,000 * (1.10 * 1.10 * 1.10 * 1.10 * 1.10 * 1.10) P(6) = 330,000 * (1.771561) P(6) = 584,595.13Round answer if necessary: Round the answer to the nearest whole number if necessary. The amount of CO2 emissions after 6 years is approximately 584,595 metric tons.

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Belmont is a growing industrial town. Every year, the level of $\text{CO}_2$ emissions from the town increases by $10\%$ . If the town produced $330,000$ metric tons of $\text{CO}_2$ this year, how much will be produced $6$ years in the future? $\newline$ If necessary, round your answer to the nearest whole number. $\newline$ ____ metric tons $\newline$

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Algebra 1

Exponential growth and decay: word problems

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Q. Belmont is a growing industrial town. Every year, the level of

\text{CO}_2

emissions from the town increases by

10\%

. If the town produced

330,000

metric tons of

\text{CO}_2

this year, how much will be produced

6

years in the future?

\newline

If necessary, round your answer to the nearest whole number.

\newline

____ metric tons

\newline

Identify initial CO_$2$ emissions: Identify the initial amount of CO_$2$ emissions and the rate of increase. $\newline$ The initial amount of CO_$2$ emissions is $330,000$ metric tons, and the rate of increase is $10\%$ per year.
Determine growth formula: Determine the formula for exponential growth. $\newline$ The formula for exponential growth is $P(t) = P_0 \times (1 + r)^t$ , where $P(t)$ is the amount after time $t$ , $P_0$ is the initial amount, $r$ is the rate of increase, and $t$ is the time in years.
Convert rate to decimal: Convert the rate of increase to a decimal. A $10\%$ increase is the same as multiplying by $1.10$ , so $r = 0.10$ .
Substitute values into formula: Substitute the values into the exponential growth formula. $P(t) = 330,000 \times (1 + 0.10)^6$
Calculate CO $2$ emissions after $6$ years: Calculate the amount of CO $2$ emissions after $6$ years. $\newline$ $P(6) = 330,000 \times (1.10)^6$ $\newline$ $P(6) = 330,000 \times (1.10 \times 1.10 \times 1.10 \times 1.10 \times 1.10 \times 1.10)$ $\newline$ $P(6) = 330,000 \times (1.771561)$ $\newline$ $P(6) = 584,595.13$
Round answer if necessary: Round the answer to the nearest whole number if necessary. $\newline$ The amount of $\text{CO}_2$ emissions after $6$ years is approximately $584,595$ metric tons.