Question

Which function can be used to find the number of cells of bacteria in the population at time t

Answer 1

db / dt = kb

this becomes b(t) = Ce^(kt)

C = 100, the initial population

P(1) = 420 = 100 e^(1k)

4.2 = e^k

ln 4.2 = k

a) thus, b(t) = 100 e^(t ln 4.2)

b) b(3) = 100 e^(3 ln 4.2)

c) growth constant will still be ln 4.2 (constant percentage of populatioin)

d) 10000 = 100 e^(t ln 4.2)

100 = e^(t ln 4.2)

ln 100 = t ln 4.2

t = ln 100 / ln 4.2

Explanation: