Question

the figure below shows the total number $p(t)$ of covid - 19 cases in montana on or before day $t$, where $t = 0$ is march 1, 2020.1
montana, total cases $p$
100,000|
60,000|
20,000|
100 200 300 365 $t$(days)
1smoothed from jhu csse covid - 19 data at github.com/cssegisanddata/covid - 19, accessed march 1, 2021.
(a) which of the following is the approximate $t$-value of an inflection point of $p(t)$?
$t = 130$
$t = 220$
$t = 260$
$t = 330$

Explanation:

Step1: Recall inflection - point concept

An inflection point of a function is where the concavity changes. On a graph, it is where the curve changes from being concave - up to concave - down or vice - versa.

Step2: Analyze the graph of \(P(t)\)

Looking at the graph of \(P(t)\), we can see that the curve is concave - up initially (curving upwards like a cup) and then changes to concave - down (curving downwards like an upside - down cup). The point where this change occurs is around \(t = 220\).

Answer:

\(t = 220\)