(a) explain the meaning of the statement r(10) = 1297. the statement tells us that on april 10, there were…

(a) explain the meaning of the statement r(10) = 1297. the statement tells us that on april 10, there were in total 1297 covid - 19 cases in california. on april 10, 12.97% of the cases in california were new cases on that day. on april 10, 1.297% of the cases in california were new cases on that day. on april 10, the total number of covid - 19 cases in california was increasing at a rate of 1297 cases per day. there were 1297 new covid - 19 cases in california between april 1 and april 10. (b) if ∫15^22 r(t)dt = 8905, give the units of the 15, the 22, and the 8905. units of the 15: units of the 22: units of the 8905:

(a) explain the meaning of the statement r(10) = 1297. the statement tells us that on april 10, there were in total 1297 covid - 19 cases in california. on april 10, 12.97% of the cases in california were new cases on that day. on april 10, 1.297% of the cases in california were new cases on that day. on april 10, the total number of covid - 19 cases in california was increasing at a rate of 1297 cases per day. there were 1297 new covid - 19 cases in california between april 1 and april 10. (b) if ∫15^22 r(t)dt = 8905, give the units of the 15, the 22, and the 8905. units of the 15: units of the 22: units of the 8905:

Answer

Explanation:

Step1: Analyze the meaning of $r(10) = 1297$

The function $r(t)$ likely represents the rate - of - change of the number of Covid - 19 cases with respect to time $t$. When $t = 10$, $r(10)=1297$ means the rate of change of the total number of Covid - 19 cases at time $t = 10$. So on April 10, the total number of Covid - 19 cases in California was increasing at a rate of 1297 cases per day.

Step2: Analyze the units of definite integral $\int_{15}^{22}r(t)dt$

The definite integral $\int_{a}^{b}r(t)dt$ represents the net change in the quantity that $r(t)$ is the rate of change of. Since $r(t)$ has units of cases per day (from part (a)), and the integral is $\int_{15}^{22}r(t)dt$, the limits of integration 15 and 22 represent days, and the value 8905 represents the net number of cases.

Answer:

(a) on April 10, the total number of Covid - 19 cases in California was increasing at a rate of 1297 cases per day. (b) Units of the 15: days Units of the 22: days Units of the 8905: Covid - 19 cases