Question

natasha is observing the growth of a population of bacteria. she started out with 250 bacteria cells. the population of bacteria quadruples every hour. use x to represent the number of hours and y to represent the population of bacteria. enter an equation in the box that represents this scenario.

Explanation:

Step1: Identify the general form of an exponential function

The general form of an exponential function is \(y = a\cdot b^{x}\), where \(a\) is the initial value and \(b\) is the base (the factor by which the quantity changes per unit of \(x\)).

Step2: Determine the values of \(a\) and \(b\)

Given that the initial number of bacteria cells \(a = 250\). The population quadruples every hour. Quadrupling means multiplying by \(4\), so \(b = 4\).

Step3: Substitute \(a\) and \(b\) into the exponential function

Substituting \(a = 250\) and \(b = 4\) into \(y=a\cdot b^{x}\), we get \(y = 250\cdot4^{x}\)

Answer:

\(y = 250\cdot4^{x}\)