Question

A scientist begins an experiment with a petri dish containing a culture of bacteria cells and records the cell growth every hour. At 1 hour, the bacteria had grown to 880 cells, and at 2 hours, had grown to 3,520 cells. Which function can be used to represent the relationship between the number of bacteria cells, y, and the time in hours, x?

Answer 1

These are the choices y = 4 x y = 220(4) x y = 880(4) x y = 880(0.25) x Right..?

Answer 2

Answer: Hello!

we know that in the first hour, we had 880 cells, and in the second hour we have 3520 cells. The first step is see how much the population changed in this one hour, this can be done by looking into the quotient:

3520/880 = 4

then the population of cells cuatriplied in one hour, and is safe to asume that every hour that pases, the population will catriplied again.

so if the populationat hour 1 is: 880

at hour 2 is: 4*880

at hour 3 is = 4*4*880 and so on.

This can be described with an exponential function as follows

`P(t) = 880*4^(x-1)`

where 880 is the initial population, and x is represents the hours.