To find the rate of change of the given savings function, let's break down the function and analyze its components.
The given function for Ali's savings is:
[tex]\[ y = 5x + 25 \][/tex]
This is a linear function of the form [tex]\(y = mx + b\)[/tex], where:
- [tex]\(y\)[/tex] represents the total amount of money saved.
- [tex]\(x\)[/tex] represents the number of weeks.
- [tex]\(m\)[/tex] is the rate of change or the slope.
- [tex]\(b\)[/tex] is the y-intercept, which represents the initial amount of money (before any saving occurs).
In the function [tex]\(y = 5x + 25\)[/tex]:
- The coefficient of [tex]\(x\)[/tex] is 5. This coefficient (5) represents the rate of change of the function.
Thus, the rate of change of Ali's savings function is:
[tex]\[ 5 \][/tex]
Therefore, the rate of change of this function is [tex]\(\boxed{5}\)[/tex].
