Question

A curve and two labeled points on the curve are plotted in quadrant 1 of a coordinate plane.
Given the graph of the exponential equation, write the correct exponential equation for the graph.

(1 point)
Responses

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

y=3(23)x
y equals 3 left parenthesis Start Fraction 2 over 3 End Fraction right parenthesis superscript x baseline

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

y=2(32)x

Answer 1

To determine the correct exponential equation for the curve, we can analyze the general form of an exponential equation, which is typically represented as:

\[ y = ab^x \]

where:
- \( a \) is the initial value (the y-intercept),
- \( b \) is the base which represents the growth factor.

Without seeing the specific graph and the labeled points, it's difficult to explicitly identify which equation is correct. However, here's a breakdown of the options you’ve provided:

1. \( y = 32(3)^x \)
2. \( y = \frac{3}{2}(3)^x \)
3. \( y = 3(2^3)^x \)
4. \( y = 3\left(\frac{2}{3}\right)^x \)
5. \( y = 3(3^2)^x \)
6. \( y = 2(3^2)^x \)

The optimal approach would involve checking the structure of these equations against the curve's characteristics. For example, if the points show growth and the base \( b \) is greater than 1, it's likely that the equation models exponential growth. If \( b \) is less than 1, then it indicates decay.

If you know the given points on the curve or have more context on the curve's behavior (like what happens as x increases), that would greatly help in selecting the appropriate equation.

Otherwise, without that information, I can't definitively tell you which option is the right equation for the graph in question. If you have specific points or details about the curve, please share them!