Question

Use the image to answer the question.

A curve and two labeled points on the curve are plotted in quadrant 1 of a coordinate plane.
The values on the x-axis range from 0 to 3 in increments of 1. The values on the y-axis range from 0 to 8 in increments of 1. A curve with an arrow on the right end begins at a point plotted on the y-axis labeled left parenthesis 0 comma 3 right parenthesis. The curve slopes upward from left to right, passing through another plotted point labeled left parenthesis 1 comma 4.5 right parenthesis. The curve continues to rise through quadrant 1, passing through the following approximate points: left parenthesis 1.5 comma 5.5 right parenthesis and left parenthesis 2.4 comma 8 right parenthesis.


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=2(3/2)^(x)

y equals 2 left parenthesis Start Fraction 3 over 2 End Fraction right parenthesis superscript x baseline

y=3/2(3)^(x)

y equals Start Fraction 3 over 2 End Fraction left parenthesis 3 right parenthesis superscript x baseline

Answer 1

y = 3(3/2)^x

Reason: y-intercept is 3 so a = 3, the graph increases so base > 1, and at x = 1 gives y = 3*(3/2) = 4.5 which matches the plotted point (1, 4.5).