The number of bacteria in a science experiment quadruples every 5 days. There are currently 25 bacteria.

Question

a. What is the daily growth rate of the speciment?

b. Write an exponential function that models this situation.

c. How many bacteria are there 7 days from now?

Answer 1

The growth control factor is 4^(t/5). This can also be written 2^(2t/5)=2^0.4t.

The function f(t)=p₀2^(0.4t) where p₀=25 the initial number of bacteria.

When t=1, f(1)=1.32p₀ so the daily growth rate is 1.32 approx (a).

(b) f(t)=p₀2^(0.4t) where p₀=25 the initial number of bacteria.

(c) f(7)=25×2^2.8=174.