Answer :
Answer:
Step-by-step explanation:
To find an equation that relates the age \( a \) of the sea sponge (in years) to its height \( h \) (in centimeters), we can use the points provided: \( (4, 8), (8, 16), (10, 20) \).
These points suggest a linear relationship between age and height. We can find the slope \( m \) of the line using two points, for example, \( (4, 8) \) and \( (10, 20) \):
\[ m = \frac{20 - 8}{10 - 4} = \frac{12}{6} = 2 \]
Now that we have the slope \( m = 2 \), we can use the point-slope form of the equation of a line:
\[ h - h_1 = m(a - a_1) \]
Let's use point \( (4, 8) \) to find the equation:
\[ h - 8 = 2(a - 4) \]
Now, solve for \( a \):
\[ h - 8 = 2a - 8 \]
\[ h = 2a \]
Therefore, the equation that relates the age \( a \) of the sea sponge to its height \( h \) is \( \boxed{a = \frac{h}{2}} \).
This equation indicates that the age \( a \) of the sponge is half of its height \( h \) in centimeters.
Answer:
The equation that Noah can use to find the age (a) of the sea sponge based on its height (h) in centimeters is:
a = 0.5h
This equation can be derived from the given information:
- The three data points provided are (4, 8), (8, 16), and (10, 20).
- These points show that as the age (a) increases by 2 years, the height (h) increases by 4 cm.
- Therefore, the rate of growth is 2 cm per year, or 0.5 years per cm.
- This linear relationship can be expressed as the equation a = 0.5h, where a is the age in years and h is the height in centimeters.
