Answer:
The question seems to be incomplete, so i will think that this is a linear equation, where we can find the velocity at which she moves, and also her initial position.
A linear relationship can be written as:
y = a*x + b
where a is the slope and b is the y-axis intercept.
For a line that passes through the points (x1, y1) and (x2, y2), the slope can be written as:
a = (y2 - y1)/(x2 - x1).
In this case we have two points:
"After 2 minutes, she was 100 steps from the bottom floor."
this can be represented with the point: (2min, 100 steps)
" After 5 minutes she was 196 steps from the bottom floor"
This can be represented with the point (5min, 196 steps)
With this, we can find the slope of this equation:
a = (196 steps - 100 steps)/(5min - 2min) = 96steps/3min = 32 steps/min
This means that she does 32 steps in one minute.
Then we can write her positon equation as:
y = (32steps/min)*x + b
where x represents the time, and b is her initial position.
If we replace x by 2 min, and y for 100 steps, we get:
100steps = (32steps/min)*2min + b
100 steps = 64 steps + b
100 steps - 64 steps = b = 36 steps.
This means that she started to take the stairs 36 steps from the bottom floor.
