The numbr N of bacteria present in a culture at time t (in hours) obeys the model n(t()=1000e 0.01t

a)Determine the number of bacteria at t=0 hours

b)what is the growth rate of the bacteria?

c) Graph the function using a graphing utility

d)What is the population after 4 hours

e) When will the bacteria reach 1700

f)When will the number of bacteria double

Solution:

(a) t=0, N(0) = 1000

(b) growth rate = N'(t) = 10e^(0.01t), it varies with time t.

(c) We choose the points (0,1000), (10, 1105), and draw an exponential curve.

(d) N(4) = 1000*e^(0.04) = 1041

(e) N(t) = 1700, 1000*e^(0.01t)=1700, t = 54, so 54 hours later it reaches 1700

(f) N(t) = 2000, 1000*e^(0.01t)=1700, t = 70, so 70 hours later it doubles