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.

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.

vertical asymptote .

horizontal asymptote .

step-by-step explanation:

given function is .

vertical asymptote is given by setting

denominator =0

when degree of numerator and denominator are same then divide first term of numerator by first term of denominator to get horizontal asymptote.

good luck on ur quiz test or homework. have a good day : )