Question

Based on the patterns in the data table, determine what kind of function models the simulation and write the equation?

Answer 1

This is a case of population growth.

The growth can by modeled using the formula:

$P=P_0b^t$

Where:

$\begin{gathered} P_0\text{ is the initial population} \\ b\text{ is the growth factor} \\ t\text{ is the number of time periods} \end{gathered}$

In this case,

$\begin{gathered} P_0=2 \\ b=4 \\ \text{ The time period is }3\text{ weeks} \end{gathered}$

Therefore, the required equation is given by:

$\begin{gathered} y=2\times2^t \\ y=2^{t+1} \end{gathered}$

Therefore, the required equation is:

$y=2^{t+1}$