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? If so, is it linear? Explain your
reasoning.

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 dayfrom 5 to 10 then fr class=

Respuesta :

Answer:

Yes, but it is not linear. It is exponential :  [tex]f(x) = 5\cdot 2^{x-1}[/tex]

Step-by-step explanation:

On the first day we have 5 bacteria.

On the second day we will have 5*2 = 10 bacteria.

On the third day we will have 10*2 = 5*2*2 = 5*2^2 = 20 bacteria.

On the fourth day we will have 20*2 = 5*2*2*2 = 5*2^3 = 40 bacteria.

We can see that

                                                [tex]f(x) = 5\cdot 2^{x-1}[/tex],

where x is a number of days and f(x) gives us the number of bacteria.