the cost of a particular private school begins with a one - time initiation fee of $2000, plus annual…
the cost of a particular private school begins with a one - time initiation fee of $2000, plus annual tuition of $5,000. this situation can be modeled by a linear function. identify the independent and dependent variables. draw a graph of the function, then use the graph to find the cost to attend this school for 6 years. is a linear model reasonable for this situation? the number of years is the independent variable. the cost is the dependent variable. use the graphing tool to graph the line.
Answer
Explanation:
Step1: Define the linear - function formula
The general form of a linear function is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept. In this case, the one - time initiation fee of $b = 2000$ is the y - intercept, and the annual tuition of $m = 5000$ is the slope. So the cost function $C(y)$ (where $y$ is the number of years) is $C(y)=5000y + 2000$.
Step2: Calculate the cost for 6 years
Substitute $y = 6$ into the function $C(y)=5000y + 2000$. $C(6)=5000\times6+2000$. $C(6)=30000 + 2000$. $C(6)=32000$.
Step3: Analyze the linear - model
The linear model is reasonable because the cost increases by a fixed amount ($5000$) each year, which is a characteristic of a linear relationship.
Answer:
The cost to attend the school for 6 years is $$32000$, and a linear model is reasonable for this situation.