Hello there. To solve this question, we'll need to plug in the value of x to find the value of the function in that point.
Let g(x) = 1/(2x - 4).
To evaluate g(10), we need to plug in x = 10 to the function
g(10) = 1/(2*10 - 4)
Multiply the values
g(10) = 1/(20 - 4)
Subtract the values
g(10) = 1/16.
QUESTION 2
To calculate the average rate of change of the amount of money, we'll need to use the slope formula.
The slope m of a line passing through two points (x0, y0) and (x1, y1) is given by: m = (y1-y0)/(x1-x0)
As you can see on the graph, in the 0-th month, Sarah had $200 in her account. In the 12-th month, she had $500.
Which means we have the points (0, 200) and (12, 500)
Using the slope formula, we get:
AVG = (500 - 200)/(12-0)
Subtract the values
AVG = 300/12
AVG = 25
This is the average rate of change of the amount of money. If you wanted the instantaneous rate of change, we would be talking about derivatives. In this case, the values would be equal since we dealing with a line and the slope is the leading coefficient of the line equation.