Question

26. The population of a bacteria colony is modelled by the function p(t) = 200 + 20t - t^2, where t is time, in hours, t >= 0, and p is the number of bacteria, in thousands. a) Determine the growth rate of the bacteria population at each of the following times. i) 3 h ii) 8 h iii) 13 h iv) 18 h b) What are the implications of the growth rates in part a)? c) Determine the equation of the tangent to p(t) at the point corresponding to t = 8. d) When does the bacteria population stop growing? What is the population at this time? e) Graph the growth function and its derivative. Describe how each graph reflects the rate of change of the bacteria population. f) Determine the time interval over which the bacteria population i) increases ii) decreases

          26. The population of a bacteria colony is modelled by the function p(t) = 200 + 20t - t^2, where t is time, in hours, t >= 0, and p is the number of bacteria, in thousands.
a) Determine the growth rate of the bacteria population at each of the following times.
i) 3 h ii) 8 h iii) 13 h iv) 18 h
b) What are the implications of the growth rates in part a)?
c) Determine the equation of the tangent to p(t) at the point corresponding to t = 8.
d) When does the bacteria population stop growing? What is the population at this time?
e) Graph the growth function and its derivative. Describe how each graph reflects the rate of change of the bacteria population.
f) Determine the time interval over which the bacteria population
i) increases ii) decreases

26. The population of a bacteria colony is modelled by the function p(t) = 200 + 20t - t^2, where t is time, in hours, t >= 0, and p is the number of bacteria, in thousands.
a) Determine the growth rate of the bacteria population at each of the following times.
i) 3 h ii) 8 h iii) 13 h iv) 18 h
b) What are the implications of the growth rates in part a)?
c) Determine the equation of the tangent to p(t) at the point corresponding to t = 8.
d) When does the bacteria population stop growing? What is the population at this time?
e) Graph the growth function and its derivative. Describe how each graph reflects the rate of change of the bacteria population.
f) Determine the time interval over which the bacteria population
i) increases ii) decreases

Added by Soledad G.

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