Question

A bacteria population in a petri dish doubles every 8 hours. The initial population is 500 bacteria.

(a) Write an equation to represent a function that estimates the population of bacteria after t hours.
a) P(t) = 500 * 2^(t/8)
b) P(t) = 500 * 2^(8/t)
c) P(t) = 500 * (1/2)^(t/8)
d) P(t) = 500 * (1/2)^(8/t)

Answer 1

The population of bacteria after t hours can be represented by the function:

P(t) = 500 * 2^(t/8) Option A is answer.

Step-by-step explanation:

Since the bacteria population doubles every 8 hours, we can use the exponential growth model to represent the population as a function of time. The general form of the exponential growth model is:

P(t) = A * e^(kt)

where:

P(t) is the population at time t

A is the initial population

k is the growth rate

e is the base of the natural logarithm

In this case, the initial population is 500 bacteria, and the population doubles every 8 hours, which means that the growth rate is k = ln(2)/8. Therefore, the function that represents the population of bacteria after t hours is:

P(t) = 500 * e^(ln(2)/8 * t)

Simplifying this expression, we get:

P(t) = 500 * 2^(t/8)

Therefore, the correct answer is:

P(t) = 500 * 2^(t/8)

Option A is answer.