Question

7. A running team began with 3 teammates. Each month, each runnerbrought one new runner. Which function can be used to determine thenumber of runners on the team x months after the team began runningtogether?

Answer 1

We have the following data;

A running team began with 3 teammates.

Each month, each runner, brought one new runner.

That means if we start with 3 runners,

Next month, we would have 3 + 3 ( the total each of the 3 runners brought).

That makes 6 runners.

Next month, we would have 6 + 6 ( the total each of the 6 runners brought).

That makes 12 runners.

A function that can be used to model the number of runners "N" is;

$N=3(2)^x$

Where x is the number of months that have elapsed after the team started running together.

Let's check the validity of this function.

$\begin{gathered} N=3(2)^x \\ \text{when they just started, x = 0, and thus;} \\ N=3(2)^0=3\text{ runners. } \\ \text{after one month , x= 1} \\ N=3(2)^1=6\text{ runners.} \\ \text{after 2 months, x = 2} \\ N=3(2)^2=12\text{ runners.} \\ \text{and so on.} \end{gathered}$

We can see that the function can be used to determine the number of runners after any number of months x.ne

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