Question

Suppose that the number of bacteria in a dish increases by 50% every four hours. There are 64 bacteria initially. Write a function that describes the number of bacteria after t hours have passed.

n(t)=

Answer 1

We are going to use exponential function. The population growth is mostly formulated as
P = P₀b^(kt)
where
P₀ = initial population
b = base number
k = proportionality constant
t = time
Given P₀ = 64. The base number is increased by 50%, in this case, 1+0.50=1.50. Yet every four hours, this will be proportionality constant. Pluging in the values, we have the function:
P = 64(1.50)^(4t)