Question

Use the graph to fill in the missing elements of the exponential growth equation.
the main points are (0,4) (1,7.6) (2,14.44)
(1 point)
y=_(_)^x

Answer 1

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:

1. 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:

\( y = 4(1.9)^x \)