Question
The weight of a baby elephant shown in the table where tea is the number of weeks of growth 10 weeks 0 1 2 3 4 5 w in pounds 210 231 to 52 273 294 315 which equation shows how to calculate each rate of change for intervals 1 to 2
Answers
GPT-4o mini
To calculate the rate of change of the weight of the baby elephant for the interval from week 1 to week 2, you need to determine the weight at these weeks and then use the rate of change formula.
From your table, it looks like the weights are:
- At week 1: 231 pounds
- At week 2: 252 pounds
The formula for the rate of change \( R \) between two points is:
\[
R = \frac{f(b) - f(a)}{b - a}
\]
where:
- \( f(a) \) is the weight at the starting point (week 1),
- \( f(b) \) is the weight at the final point (week 2),
- \( a \) is the starting point (1),
- \( b \) is the final point (2).
Plugging in the values:
\[
R = \frac{252 - 231}{2 - 1} = \frac{21}{1} = 21
\]
Therefore, the rate of change of the baby elephant's weight from week 1 to week 2 is 21 pounds per week.
The equation you would use to calculate the rate of change for that interval can therefore be represented as:
\[
R = \frac{w(2) - w(1)}{2 - 1}
\]
Where:
- \( w(2) = 252 \)
- \( w(1) = 231 \)
From your table, it looks like the weights are:
- At week 1: 231 pounds
- At week 2: 252 pounds
The formula for the rate of change \( R \) between two points is:
\[
R = \frac{f(b) - f(a)}{b - a}
\]
where:
- \( f(a) \) is the weight at the starting point (week 1),
- \( f(b) \) is the weight at the final point (week 2),
- \( a \) is the starting point (1),
- \( b \) is the final point (2).
Plugging in the values:
\[
R = \frac{252 - 231}{2 - 1} = \frac{21}{1} = 21
\]
Therefore, the rate of change of the baby elephant's weight from week 1 to week 2 is 21 pounds per week.
The equation you would use to calculate the rate of change for that interval can therefore be represented as:
\[
R = \frac{w(2) - w(1)}{2 - 1}
\]
Where:
- \( w(2) = 252 \)
- \( w(1) = 231 \)