To find the parameters of the exponential growth equation \( y = a(b)^x \), we need to determine the values of \( a \) and \( b \) using the points provided: (0, 4), (1, 7.6), and (2, 14.44).
From the point (0, 4):
\[ y = a(b)^0 = a(1) = a \]
Thus, \( a = 4 \).
Next, we can use the other points to find \( b \). We can set up equations using the remaining points.
Using the point (1, 7.6):
\[ y = a(b)^1 \] Substituting in \( a \):
\[ 7.6 = 4(b) \] Solving for \( b \):
\[ b = \frac{7.6}{4} = 1.9 \]
Now we can use point (2, 14.44) to check our work:
\[ y = a(b)^2 \] Substituting \( a \) and \( b \):
\[ 14.44 = 4(1.9)^2 \]
Calculating \( (1.9)^2 \):
\[ 1.9^2 = 3.61 \]
Now calculate \( 4(3.61) \):
\[ 4 \times 3.61 = 14.44 \]
This matches the point (2, 14.44), confirming that our values are correct.
Thus, the exponential growth equation is:
\[ y = 4(1.9)^x \]
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