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 flu 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 flu 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 flu 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 flu 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 flu 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 flu 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.
Use the information in the following table to find h' (a) at the given value for a.
x|f(x) g(x) f'(x) g(x)
0
0
0
4
3
1
4
4
3
0
2
7
1
2
7
3
3
1
2
9
4
0
4
5
7
h(x) = f(g(x)); a = 0
h' (0) =
Use the information in the following table to find h' (a) at the given value for a.
x f(x) g(x) f'(x) g'(x)
0
0
3
2
1
1
0
0
2
0
2
43
22
4
3
3
2
3
1
1
4
1
2
0
4
2
h(x) = (1/(2) ²;
9(x)
h' (3)=
=
; a=3
The position of a moving hockey puck after t seconds is s(t) = tan
a. Find the velocity of the hockey puck at any time t.
v(t)
=====
b. Find the acceleration of the puck at any time t.
-1
a (t)
=
(t) where s is in meters.
c. Evaluate v(t) and a (t) for t = 1, 4, and 5 seconds. Round to 4 decimal places, if necessary.
v (1)
v (4)
v (5)
a (1)
=
=
=
=
a (4) =
a (5) =
d. What conclusion can be drawn from the results in the previous part?
○ The hockey puck is decelerating/slowing down at 1, 4, and 5 seconds
○ The hockey puck has a constant velocity/speed at 1, 4, and 5 seconds
○ The hockey puck is accelerating/speeding up at 1, 4, and 5 seconds
College Algebra with Modeling & Visualization (5th Edition)
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