To fill in the missing elements of the exponential growth equation in the form \( y = a(b)^x \), we'll use the provided points from the graph.
From the points given:
- At \( x = 0 \), \( y = 4 \).
- This gives us that \( a = 4 \) because \( y = a(b)^0 = a \cdot 1\).
To find \( b \), we can use another point. Let's take the point \( (1, 7.6) \):
\[ y = 4(b)^1 \] \[ 7.6 = 4b \] \[ b = \frac{7.6}{4} = 1.9 \]
Now, let's check the other point \((2, 14.44)\) to verify if the values are consistent:
\[ y = 4(b)^2 \] Substituting \( b = 1.9 \): \[ y = 4(1.9)^2 \] Calculating \( (1.9)^2 = 3.61 \): \[ y = 4 \cdot 3.61 = 14.44 \]
Since the calculated value matches the point \( (2, 14.44) \), our values are correct.
Thus, the exponential growth equation can be filled in as:
\( y = 4(1.9)^x \)
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