Subjects algebra

Data Relationships

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1. Problem 15: Volume of gas tank and cost to fill the tank. The cost to fill the tank is directly proportional to the volume of the gas tank. Let $V$ be the volume of the gas tank and $C$ be the cost to fill it. Then, $C = kV$ where $k$ is the cost per unit volume. 2. Problem 16: Time (years from 1960 to 2015) and salaries of working professionals. Salaries generally increase over time, so we expect a positive correlation. Let $t$ be years since 1960 and $S$ be salary. A linear model could be $S = mt + b$ where $m$ is the rate of increase and $b$ is the starting salary. 3. Problem 17: Time (years from 1960 to 2010) and average global temperature. Global temperature tends to increase over time due to climate change. Let $t$ be years since 1960 and $T$ be temperature. Model: $T = mt + b$ with positive $m$. 4. Problem 18: Area of shelves and number of books that can be arranged. Number of books is proportional to shelf area. Let $A$ be area and $N$ be number of books. Model: $N = kA$. 5. Problem 19: Distance from one place to another and travel fare. Travel fare is proportional to distance. Let $d$ be distance and $F$ be fare. Model: $F = kd$. 6. Problem 20: Rate of pedalling a bicycle and burning of calories. Calories burned increase with pedalling rate. Let $r$ be pedalling rate and $C$ be calories burned. Model: $C = kr$. 7. Problem 21: Petrol mileage of car and cost of driving 900 kilometers. Cost depends on distance and mileage. Let $m$ be mileage (km per liter), $p$ be price per liter, and $C$ be cost. Fuel needed: $\frac{900}{m}$ liters. Cost: $C = p \times \frac{900}{m}$. 8. Problem 22: Annual percentage rate (APR) and balance in savings account after 10 years. Balance grows exponentially with APR. Let $P$ be principal, $r$ be APR (as decimal), $n=10$ years, $B$ be balance. Model: $$B = P(1+r)^{10}$$ Final answers are the models above.