the function m(w)=-25w+2500 models the amount of money in a safe, in dollars, w weeks after lori learned the combination to the safe.
what is the meaning of the x-intercept?
A)there was 100$ in the safe when lori learned the combination<---
B)there was 2500$ in the safe when lori learned the combination.
C)there will be no money in the safe after lori learned the combination.
D)there will be no money in the safe 2500 weeks after lori learned the combination.
so whats the answer?
Actually, it's the w-intercept in this case.
At any rate, at the intercept, m(w)=0. That is, no money remains.
To find the meaning of the x-intercept of the given function, we first need to understand what the x-intercept represents in the context of the problem.
The x-intercept of a function is the point where the graph of the function intersects or crosses the x-axis. Mathematically, it is the value of x for which y (the function's output or value) is equal to zero.
In the given function m(w) = -25w + 2500, we can find the x-intercept by setting m(w) = 0 and solving for w:
0 = -25w + 2500
To solve for w, we can isolate w on one side:
25w = 2500
w = 2500/25
w = 100
So the x-intercept of the function m(w) = -25w + 2500 is w = 100.
Now, let's determine the meaning of this x-intercept choice by evaluating the options:
A) There was $100 in the safe when Lori learned the combination - This is incorrect because the x-intercept represents the time at which the money in the safe becomes zero, not the initial amount.
B) There was $2500 in the safe when Lori learned the combination - This is incorrect because the x-intercept does not represent the initial amount of money; it represents the time at which the safe becomes empty.
C) There will be no money in the safe after Lori learned the combination - This is a possible interpretation because the x-intercept represents the time at which the safe becomes empty.
D) There will be no money in the safe 2500 weeks after Lori learned the combination - This is incorrect because the x-intercept represents the time at which the safe becomes empty, not a fixed amount of weeks after Lori learned the combination.
Therefore, the correct answer is C) there will be no money in the safe after Lori learned the combination.