Susie plans to run 2 miles per day the first week and then increase the daily distance by a half a mile each of the following we
eks. How long before the marathon should she start? There are many ways to approach this problem. Some include, make a table, write a function, create ordered pairs...
1. Identify and label the variables.
2.Make a table for up to 6 weeks to see a pattern.
3. Write an equation to represent the nth term of the sequence.
4. If the pattern continues during which week will she run 10 miles per day?
5. Is it reasonable to think that this pattern will continue indefinitely, explain?
6. How long before the marathon should she start?
Due to length restrictions, we kindly invite to see the explanation below to know the answer with respect to each component of the question concerning linear equations.
<h3>How to determine a linear equation describing the daily distance of a runner</h3>
In this question we need to derive an expression of the <em>daily</em> distance as a function of time. Now we proceed to complete the components:
<em>Linear</em> equations have an <em>independent</em> variable (t - time) and a dependent variable (x - daily distance).
We notice that the daily distance increases linearly in time, then then we have the following pattern:
t 1 2 3 4 5 6 x 2 2.5 3 3.5 4 4.5
The equation that represents the n-th term of the sequence is x(n) = 2 + 0.5 · (n - 1).
It is not reasonable to think that pattern will continue indefinitely as it is witnessed in the difficulties experimented by <em>fastest</em> runners in the world to increase their <em>peak</em> speeds.
A marathon has a distance of 26 miles, then we must solve the following equation: