Question

Lin counts 5 bacteria under a microscope. She counts them again each day for four days, and finds that the number of bacteria doubled each day—from 5 to 10, then from 10 to 20, and so on.​​​​​​

Is the population of bacteria a function of the number of days? Explain your reasoning.

Answer 1

Answer: Yes, this is a function, and the function is:

population = y = f(d) = 5*(2)^d

Explanation:

If the population doubles each day, we will have an exponential growth, that can be written as

f(d) = A*(r)^d

Where:

A is the initial population. (in this case 5)

r is the rate of growth.

d is our variable, in this case the number of days

then:

f(d) = 5*(r)^d

such that:

f(0) = 5*(r)^0 = 5

after one day, we should have the double of 5, this is 10:

f(1) = 10 = 5*(r)^1 = 5*r

10 = 5*r

10/5 = r

2 = r

Then the equation that tells the population of bacteria is:

y = f(d) = 5*(2)^d (at least for the first four days, we do not know what happens after that)

Is the population of bacteria a function of the number of days?

Yes, this is a function because for each input d, we have only one output y.