Question

Given the graph of the exponential equation, write the correct exponential equation for the graph passing through the points (0, 3) and (1, 4.5)

Answer 1

To find the exponential equation of the form \( y = ab^x \) that passes through the points (0, 3) and (1, 4.5), we can follow these steps:

1. **Use the point (0, 3)**: When \( x = 0 \), the equation becomes:
\[
y = ab^0 = a
\]
Thus, \( a = 3 \).

2. **Use the point (1, 4.5)**: Substitute \( a \) into the equation using the point (1, 4.5):
\[
4.5 = 3b^1
\]
This simplifies to:
\[
4.5 = 3b
\]
Solving for \( b \):
\[
b = \frac{4.5}{3} = 1.5
\]

3. **Write the final equation**: Now substitute \( a \) and \( b \) back into the equation:
\[
y = 3(1.5)^x
\]

Thus, the exponential equation for the graph that passes through the points (0, 3) and (1, 4.5) is:
\[
y = 3(1.5)^x
\]