Question

mathematics ii a thayer fall 25
comparing exponential, linear, and quadratic growth
the graph shows a linear function and an exponential function.
what is the minimum y-value after which the exponential function will always be greater than the linear function?
options:
y=4
y=3
y=1
y=5
(c) 59.34

Explanation:

Step1: Analyze the Graph

The graph has a linear function (red line) and an exponential function (blue curve) intersecting at \((1, 4)\). For \(x > 1\), we need to see when the exponential function is always above the linear function.

Step2: Determine the Minimum \(y\)-value

Looking at the intersection point \((1, 4)\), after \(x = 1\) (or at \(y = 4\) as the starting point of the region where exponential is above linear), we check the options. The minimum \(y\)-value after which exponential is always greater than linear is when \(y = 4\) (since at \(x = 1\), both are 4, and for \(x > 1\) (or \(y\) values related to \(x > 1\)) the exponential starts to be above, so the minimum \(y\)-value here is 4.

Answer:

\(y = 4\)