Question

Use the image to answer the question. Use the graph to fill in the missing elements of the exponential growth equation. (1 point) y= ()x 0,4 1,7.6 2,14.44

Answer 1

To fill in the missing elements of the exponential growth equation based on the points given (0, 4), (1, 7.6), and (2, 14.44), we start with the general form of the exponential growth equation:

\[ y = a \cdot b^x \]

Where:
- \( a \) is the initial value (when \( x = 0 \)),
- \( b \) is the growth factor.

From the point (0, 4), we can determine the value of \( a \):

- When \( x = 0 \), \( y = 4 \), so \( a = 4 \).

Now, we can write the equation as:

\[ y = 4 \cdot b^x \]

Next, we can use one of the other points to find the growth factor \( b \). Using the point (1, 7.6):

\[ 7.6 = 4 \cdot b^1 \]

To solve for \( b \):

1. Divide both sides by 4:
\[
b = \frac{7.6}{4} = 1.9
\]

Now, we have \( a = 4 \) and \( b = 1.9 \). We can also check with the next point (2, 14.44):

Using the equation:
\[ y = 4 \cdot (1.9)^2 \]

Calculating:
\[ 4 \cdot 1.9^2 = 4 \cdot 3.61 = 14.44 \]
This checks out.

Thus, the full exponential growth equation with the missing elements filled in is:

\[ y = 4 \cdot 1.9^x \]