Question

Taska. In a carefully controlled biology lab, a population of 100 bacteria reproducesvia binary fission. That is, every hour, on the hour, each bacteria splits into two bacteria.Assuming no bacteria deaths, find an expression for the number P(1) of bacteria in thepopulation after t hours.b. In the next lab over, a population of protists reproduces hourly according to multiplefission. The function which gives the population of protists after t hours isP(t) = 50 . 3'.Interpret the significance of the numbers 50 and 3 in the context of the biologicalexperiment.

Answer 1

a)

`P(t)=100\cdot3^t`

b) 50 is the initial population of protists, that is, the number of protists at the beginning of the experiment.

3 is the growth rate which is the factor by which the population of protists grows every hour.

Step-by-step explanation:

An exponential function is generally given as;

`f(t)=a\cdot b^t`

where a = initial or starting amount

b = the growth rate which is the quantity by which the initial amount is

multiplied each time t is increased by 1

t = time

a) Given an initial population of bacteria as 100 and we're told that every hour, each bacteria splits into two, we can deduce that;

a = initial amount

b = growth rate = 2

We can go ahead and write the required expression as;

`P(t)=100\cdot2^t`

b) Given the below;

`P(t)=50\cdot3^t`

If we compare the given function with the exponential function stated above, we can see that;

a = initial amount 50

This means that 50 is the initial population of protists, that is, the number of protists at the beginning of the experiment.

b = growth rate = 3

This means that 3 is the growth rate which is the factor by which the population grows every hour.