Westonci.ca makes finding answers easy, with a community of experts ready to provide you with the information you seek. Discover precise answers to your questions from a wide range of experts on our user-friendly Q&A platform. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform.
Sagot :
To find the carbon-dioxide emissions [tex]\( E(t) \)[/tex] [tex]\( t \)[/tex] years from today, we need to consider the following information:
- The current emission level is 40 million tons.
- Each year, the emission is reduced by 35%.
Let's denote:
- The initial emission level as [tex]\( E_0 \)[/tex] which is 40 million tons.
- The annual reduction rate as [tex]\( r \)[/tex] which is 35%, or 0.35 in decimal form.
We need to express [tex]\( E(t) \)[/tex], which is the emission level [tex]\( t \)[/tex] years from today. Each year, the emissions are reduced to 65% of the previous year's emissions. This means that we multiply the emission level from one year by 0.65 to get the next year's emission level (since [tex]\( 100\% - 35\% = 65\% \)[/tex]).
So, every year, the emissions will be multiplied by [tex]\( 0.65 \)[/tex]:
1. After 1 year, the emission level will be [tex]\( 40 \times 0.65 \)[/tex].
2. After 2 years, it will be [tex]\( 40 \times 0.65^2 \)[/tex].
3. After [tex]\( t \)[/tex] years, it will be [tex]\( 40 \times 0.65^t \)[/tex].
Therefore, to express the carbon-dioxide emissions [tex]\( E(t) \)[/tex] [tex]\( t \)[/tex] years from now, we use the formula:
[tex]\[ E(t) = 40 \times 0.65^t \][/tex]
This is a function that describes Freedonia's carbon-dioxide emissions in million tons [tex]\( t \)[/tex] years from today.
- The current emission level is 40 million tons.
- Each year, the emission is reduced by 35%.
Let's denote:
- The initial emission level as [tex]\( E_0 \)[/tex] which is 40 million tons.
- The annual reduction rate as [tex]\( r \)[/tex] which is 35%, or 0.35 in decimal form.
We need to express [tex]\( E(t) \)[/tex], which is the emission level [tex]\( t \)[/tex] years from today. Each year, the emissions are reduced to 65% of the previous year's emissions. This means that we multiply the emission level from one year by 0.65 to get the next year's emission level (since [tex]\( 100\% - 35\% = 65\% \)[/tex]).
So, every year, the emissions will be multiplied by [tex]\( 0.65 \)[/tex]:
1. After 1 year, the emission level will be [tex]\( 40 \times 0.65 \)[/tex].
2. After 2 years, it will be [tex]\( 40 \times 0.65^2 \)[/tex].
3. After [tex]\( t \)[/tex] years, it will be [tex]\( 40 \times 0.65^t \)[/tex].
Therefore, to express the carbon-dioxide emissions [tex]\( E(t) \)[/tex] [tex]\( t \)[/tex] years from now, we use the formula:
[tex]\[ E(t) = 40 \times 0.65^t \][/tex]
This is a function that describes Freedonia's carbon-dioxide emissions in million tons [tex]\( t \)[/tex] years from today.
Thank you for trusting us with your questions. We're here to help you find accurate answers quickly and efficiently. Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Thank you for trusting Westonci.ca. Don't forget to revisit us for more accurate and insightful answers.