# Mastering Linear Functions: Real-World Applications and Problem-Solving Explore practical applications of linear functions in everyday life. Learn to model real-world scenarios, from economics to physics, using linear relationships. Enhance your problem-solving skills with our comprehensive guide.

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Examples

- The value $V$ of a classic toy car, in dollars, is given by $V + 15t = 350$, where $t$ is the age of the car. If the car was bought new 5 years ago, graph the equation and estimate the value of the car 6 years from now.
- The cost $C$, in dollars, of renting a hall for the prom is given by the formula $C(n) = 500 + 4n$, where $n$ is the number of students attending the prom. Calculate the cost of renting the hall if 70 students attend.
- Sam completes a puzzle in time $t$ (mins) is related to number of tries ($n$). The resulting equation is $t = 30 - {4 \over 5}n$ Graph the equation and estimate the time it takes him to do the puzzle on his $15^{th}$ try.
- A game rental store charges $15.00 to rent the console and the game and $3.00 per additional hour. Write the linear equation. Determine the cost of renting for 15 hours. Determine the hours if the cost was $150.
- In 1970 the population of Andyland city was 900,000, in 1995 the population of the same city had grown to 1,500,000.

i) Find the average rate of change for the population of this city from 1970 to 1995.

ii) Predict how many people will live in this city in 2015. - A car repair shop charges an hourly rate plus a fixed amount. One hour costs $70, and four hours costs $160.

i) Determine the hourly rate.

ii) Write the equation that shows the total cost ($C$) in terms of number of hours ($H$) and the fixed cost ($F$).

iii) Domain and Range. - Jack has two options when renting his car for the vacation:

Option A: $50 per day, and no extra charge per kilometre.

Option B: $35 per day, and 15 cents per kilometre.

i) Graph the options $A$ & $B$

ii) How many kilometres must Jack travel to make option $A$ the cheapest rate?