The number N ( t ) of new cases of a flu outbreak for a given city is given by N ( t ) = 5000 ⋅ 2 − 0.04 t 2 , where t is the number of months since the outbreak began. a. Find the average rate of change in the number of new nu cases between months 0 and 2, and interpret the result. Round to the nearest whole unit. b. Find the average rate of change in the number of new nu cases between months 4 and 6. and between months 10 and 12. c. Use a graphing utility to graph the function. Use the graph and the average rates of change found in parts (a) and (b) to discuss the pattern of the number of new flu cases.
The number N ( t ) of new cases of a flu outbreak for a given city is given by N ( t ) = 5000 ⋅ 2 − 0.04 t 2 , where t is the number of months since the outbreak began. a. Find the average rate of change in the number of new nu cases between months 0 and 2, and interpret the result. Round to the nearest whole unit. b. Find the average rate of change in the number of new nu cases between months 4 and 6. and between months 10 and 12. c. Use a graphing utility to graph the function. Use the graph and the average rates of change found in parts (a) and (b) to discuss the pattern of the number of new flu cases.
Solution Summary: The author calculates the average rate of change of new flu cases between months 0 and 2 of a city given by equation N(t)=5000cdot 2-0.04
of new cases of a flu outbreak for a given city is given by
N
(
t
)
=
5000
⋅
2
−
0.04
t
2
, where t is the number of months since the outbreak began.
a. Find the average rate of change in the number of new nu cases between months 0 and 2, and interpret the result. Round to the nearest whole unit.
b. Find the average rate of change in the number of new nu cases between months 4 and 6. and between months 10 and 12.
c. Use a graphing utility to graph the function. Use the graph and the average rates of change found in parts (a) and (b) to discuss the pattern of the number of new flu cases.
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.
Area Between The Curve Problem No 1 - Applications Of Definite Integration - Diploma Maths II; Author: Ekeeda;https://www.youtube.com/watch?v=q3ZU0GnGaxA;License: Standard YouTube License, CC-BY