the figure below shows the total number p(t) of covid - 19 cases in massachusetts confirmed on or before day…

the figure below shows the total number p(t) of covid - 19 cases in massachusetts confirmed on or before day t, where t = 0 is march 1, 2020; n(t) is the number of new cases on day t. use the fact that p(t)≈n(t) to draw conclusions about the graph of n(t). massachusetts, total cases p 600,000 400,000 200,000 0 100 200 300 t (days) 1smoothed from jhu csse covid - 19 data at github.com/cssegisanddata/covid - 19, accessed march 24, 2021. (a) how many peaks does n(t) have? roughly when do the peaks occur? select all correct choices. n(t) has a peak □ between t = 0 and t = 20. □ between t = 20 and t = 60. □ between t = 60 and t = 120. □ between t = 120 and t = 220. □ between t = 220 and t = 260. □ between t = 260 and t = 350. □ at t = 365. (b) which peak appears to be the largest? give a reason for your answer. the peak that appears to be the largest is the one o between t = 0 and t = 20, since p(t) was very small there, so small peaks are larger in comparison. o between t = 20 and t = 60, because p(t) climbs much more relative to the small values it has. o between t = 60 and t = 120, because the bend in p(t) is the strongest bend in the graph. o between t = 120 and t = 220, because it is the largest straight stretch in the graph of p(t). o between t = 220 and t = 260, because p(t) has large values and bends noticeably upwards for those t - values. o between t = 260 and t = 350, because the graph of p(t) is the steepest during this period. o to the right, since it is the highest point of the graph of p(t).

the figure below shows the total number p(t) of covid - 19 cases in massachusetts confirmed on or before day t, where t = 0 is march 1, 2020; n(t) is the number of new cases on day t. use the fact that p(t)≈n(t) to draw conclusions about the graph of n(t). massachusetts, total cases p 600,000 400,000 200,000 0 100 200 300 t (days) 1smoothed from jhu csse covid - 19 data at github.com/cssegisanddata/covid - 19, accessed march 24, 2021. (a) how many peaks does n(t) have? roughly when do the peaks occur? select all correct choices. n(t) has a peak □ between t = 0 and t = 20. □ between t = 20 and t = 60. □ between t = 60 and t = 120. □ between t = 120 and t = 220. □ between t = 220 and t = 260. □ between t = 260 and t = 350. □ at t = 365. (b) which peak appears to be the largest? give a reason for your answer. the peak that appears to be the largest is the one o between t = 0 and t = 20, since p(t) was very small there, so small peaks are larger in comparison. o between t = 20 and t = 60, because p(t) climbs much more relative to the small values it has. o between t = 60 and t = 120, because the bend in p(t) is the strongest bend in the graph. o between t = 120 and t = 220, because it is the largest straight stretch in the graph of p(t). o between t = 220 and t = 260, because p(t) has large values and bends noticeably upwards for those t - values. o between t = 260 and t = 350, because the graph of p(t) is the steepest during this period. o to the right, since it is the highest point of the graph of p(t).

Answer

Explanation:

Step1: Recall the relationship between $P(t)$ and $N(t)$

Since $N(t)\approx P^{\prime}(t)$, the peaks of $N(t)$ occur where the slope of $P(t)$ changes from increasing to decreasing.

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

Looking at the graph of $P(t)$, we can see that the slope of $P(t)$ changes from increasing to decreasing in the interval $t = 120$ to $t=220$. This is because in this interval, the graph of $P(t)$ goes from curving upwards (concave - up) to curving downwards (concave - down).

(a)

Answer:

$N(t)$ has a peak between $t = 120$ and $t = 220$.

(b)

Explanation:

The peak of $N(t)$ (since $N(t)\approx P^{\prime}(t)$) is largest when the change in the slope of $P(t)$ is most significant. The graph of $P(t)$ has the largest straight - stretch (where the slope is changing most rapidly) between $t = 120$ and $t = 220$.

Answer:

The peak that appears to be the largest is the one between $t = 120$ and $t = 220$, because it is the largest straight stretch in the graph of $P(t)$.