Spread of infection. Spread by skin-to-skin contact or via shared towels or clothing, methicillin-resident Staphylococcus aureus (MRSA) can easily infect growing numbers at a university. Left unchecked, the number of cases of MRSA on a university campus t weeks after the first 9 cases occur can be modeled by N ( t ) = 568.803 1 + 62.200 e − 0.092 t . ( Source : Vermont Department of Health, Epidemiology Division.) 11.8, 221.4, 547.2 a. Find the number of infected students beyond the first 9 cases after 3 weeks, 40 weeks, and 80 weeks. b. Find the rate at which the disease is spreading after 20 weeks. c. Explain why an unrestricted growth model is inappropriate but a logistic equation is appropriate for this situation. Then use a calculator to graph the equation.
Spread of infection. Spread by skin-to-skin contact or via shared towels or clothing, methicillin-resident Staphylococcus aureus (MRSA) can easily infect growing numbers at a university. Left unchecked, the number of cases of MRSA on a university campus t weeks after the first 9 cases occur can be modeled by N ( t ) = 568.803 1 + 62.200 e − 0.092 t . ( Source : Vermont Department of Health, Epidemiology Division.) 11.8, 221.4, 547.2 a. Find the number of infected students beyond the first 9 cases after 3 weeks, 40 weeks, and 80 weeks. b. Find the rate at which the disease is spreading after 20 weeks. c. Explain why an unrestricted growth model is inappropriate but a logistic equation is appropriate for this situation. Then use a calculator to graph the equation.
Solution Summary: The author calculates the number of infected students beyond first 9 cases from MRSA after 3weeks.
Spread of infection. Spread by skin-to-skin contact or via shared towels or clothing, methicillin-resident Staphylococcus aureus (MRSA) can easily infect growing numbers at a university. Left unchecked, the number of cases of MRSA on a university campus t weeks after the first 9 cases occur can be modeled by
N
(
t
)
=
568.803
1
+
62.200
e
−
0.092
t
.
(Source: Vermont Department of Health, Epidemiology Division.) 11.8, 221.4, 547.2
a. Find the number of infected students beyond the first 9 cases after 3 weeks, 40 weeks, and 80 weeks.
b. Find the rate at which the disease is spreading after 20 weeks.
c. Explain why an unrestricted growth model is inappropriate but a logistic equation is appropriate for this situation. Then use a calculator to graph the equation.
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