An orchestra buys music stands for $42 each with $298 in its bank account. Write a function rule that shows how the account balance depends on the number of stands bought. What are the initial value and rate of change of the function?
accountbalance=298-42*stands
rate of change is -42dollars/stand
To write a function rule that shows how the account balance depends on the number of stands bought, we can use the concept of linear functions.
Let's denote the number of stands bought as 'x', and the account balance as 'y'.
The cost of buying each music stand is $42, so the total cost of buying 'x' stands would be 42x.
The initial value of the function, which represents the starting account balance, is $298. This means that when no stands are bought (x = 0), the account balance is $298.
The rate of change of the function represents how the account balance changes with each additional stand purchased. In this case, for every stand purchased, $42 is deducted from the account balance.
Therefore, the function rule that shows how the account balance depends on the number of stands bought can be written as:
y = 298 - 42x
In this function, the initial value is 298 and the rate of change is -42.