Question

the graph represents lees savings account over time. analyze the function shown in the graph. describe whether the function is increasing or decreasing, calculate the rate of change, and explain what the initial value represents in this context. enter your response here chat with a tutor saved your progress a few seconds ago

Explanation:

Step1: Determine if the function is increasing or decreasing

As the months (x - values) increase, the amount of money (y - values) in the account decreases. So, the function is decreasing.

Step2: Calculate the rate of change (slope)

Use the slope formula \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let \((x_1,y_1)=(0,15)\) and \((x_2,y_2)=(10,0)\). Then \(m=\frac{0 - 15}{10 - 0}=\frac{-15}{10}=-\frac{3}{2}=-1.5\)

Step3: Explain the initial value

The initial value occurs when \(x = 0\) (the account is just opened). The point \((0,15)\) means that when Lee opened the savings account, there was \(\$15\) in it. So, the initial value represents the starting amount of money in Lee's savings account.

Answer:

The function is decreasing. The rate of change is \(-1.5\) (or \(-\frac{3}{2}\)), which means Lee's savings decrease by \(\$1.50\) per month. The initial value (\(y = 15\) when \(x = 0\)) represents the amount of money (\(\$15\)) that Lee had in the savings account when it was first opened.