Question

The graph points are (0,3) and (1,4.5). The graph is going upwards. Given the graph of the exponential equation, write the correct exponential equation for the graph.

(1 point)
Responses

y=3(3/2)x
y equals 3 left parenthesis Start Fraction 3 over 2 End Fraction right parenthesis superscript x baseline

y=3(2/3)x
y equals 3 left parenthesis Start Fraction 2 over 3 End Fraction right parenthesis superscript x baseline

y=32(3)x
y equals Start Fraction 3 over 2 End Fraction left parenthesis 3 right parenthesis superscript x baseline

y=2(3/2)x

Answer 1

To find the correct exponential equation that fits the given points (0,3) and (1,4.5), we can start by using the general form of an exponential function:

\[
y = ab^x
\]

where \( a \) is the initial value (when \( x = 0 \)) and \( b \) is the growth factor.

1. From the point \( (0,3) \), we can substitute \( x = 0 \) and \( y = 3 \):
\[
3 = ab^0 \implies a = 3
\]

2. Now the function is \( y = 3b^x \).

3. Next, we use the second point \( (1,4.5) \):
\[
4.5 = 3b^1 \implies b = \frac{4.5}{3} = \frac{3}{2}
\]

Putting it all together, we can write the equation as:
\[
y = 3 \left( \frac{3}{2} \right)^x
\]

Thus, the correct exponential equation for the graph is:

\[
\boxed{y = 3 \left( \frac{3}{2} \right)^x}
\]