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*2^t \\ y=2^(t+1) \end{gathered}`

Therefore, the required equation is:

`y=2^(t+1)`