4.
(2022·门头沟模拟)
新型冠状病毒肺炎(
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmtext%3EC%3C%2Fmtext%3E%3Cmtext%3EO%3C%2Fmtext%3E%3Cmtext%3EV%3C%2Fmtext%3E%3Cmtext%3EI%3C%2Fmtext%3E%3Cmtext%3ED%3C%2Fmtext%3E%3Cmo%3E%E2%88%92%3C%2Fmo%3E%3Cmn%3E1%3C%2Fmn%3E%3Cmn%3E9%3C%2Fmn%3E%3C%2Fmath%3E)
)严重影响了人类正常的经济与社会发展.我国政府对此给予了高度重视,采取了各种防范与控制措施,举国上下团结一心,疫情得到了有效控制.人类与病毒的斗争将是长期的,有必要研究它们的传播规律,做到有效预防与控制,防患于未然.已知某地区爆发某种传染病,当地卫生部门于4月20日起开始监控每日感染人数,若该传染病在当地的传播模型为
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3Ei%3C%2Fmi%3E%3Cmn%3E%28%3C%2Fmn%3E%3Cmi%3Et%3C%2Fmi%3E%3Cmn%3E%29%3C%2Fmn%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmfrac%3E%3Cmrow%3E%3Cmn%3E2%3C%2Fmn%3E%3Cmn%3E5%3C%2Fmn%3E%3Cmn%3E0%3C%2Fmn%3E%3Cmn%3E0%3C%2Fmn%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E1%3C%2Fmn%3E%3Cmo%3E%2B%3C%2Fmo%3E%3Cmn%3E9%3C%2Fmn%3E%3Cmsup%3E%3Cmrow%3E%3Cmtext%3Ee%3C%2Fmtext%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmo%3E%E2%88%92%3C%2Fmo%3E%3Cmtext%3E%E2%80%89%3C%2Fmtext%3E%3Cmn%3E0%3C%2Fmn%3E%3Cmn%3E.%3C%2Fmn%3E%3Cmn%3E2%3C%2Fmn%3E%3Cmi%3Et%3C%2Fmi%3E%3C%2Fmrow%3E%3C%2Fmsup%3E%3C%2Fmrow%3E%3C%2Fmfrac%3E%3C%2Fmath%3E)
(
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3Ei%3C%2Fmi%3E%3Cmn%3E%28%3C%2Fmn%3E%3Cmi%3Et%3C%2Fmi%3E%3Cmn%3E%29%3C%2Fmn%3E%3C%2Fmath%3E)
表示自4月20日开始
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3Et%3C%2Fmi%3E%3C%2Fmath%3E)
(单位:天)时刻累计感染人数,
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3Ei%3C%2Fmi%3E%3Cmn%3E%28%3C%2Fmn%3E%3Cmi%3Et%3C%2Fmi%3E%3Cmn%3E%29%3C%2Fmn%3E%3C%2Fmath%3E)
的导数
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmsup%3E%3Cmi%3Ei%3C%2Fmi%3E%3Cmn%3E%27%3C%2Fmn%3E%3C%2Fmsup%3E%3Cmn%3E%28%3C%2Fmn%3E%3Cmi%3Et%3C%2Fmi%3E%3Cmn%3E%29%3C%2Fmn%3E%3C%2Fmath%3E)
表示
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3Et%3C%2Fmi%3E%3C%2Fmath%3E)
时刻的新增病例数,
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmn%3El%3C%2Fmn%3E%3Cmn%3En%3C%2Fmn%3E%3Cmn%3E9%3C%2Fmn%3E%3Cmo%3E%E2%89%88%3C%2Fmo%3E%3Cmn%3E2%3C%2Fmn%3E%3Cmn%3E.%3C%2Fmn%3E%3Cmn%3E1%3C%2Fmn%3E%3Cmn%3E9%3C%2Fmn%3E%3Cmn%3E7%3C%2Fmn%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmath%3E)
),根据该模型推测该地区新增病例数达到顶峰的日期所在的时间段为( )