Answer: Yes, this is a function, and the function is:
population = y = f(d) = 5*(2)^d
Step-by-step 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.
