Real-World Graphing Applications

Real-World Graphing Applications

Read each question carefully and answer to the best of your ability. Show all your work for short answer questions.

1. A company's profit (P) in thousands of dollars over 't' months is modeled by the function P(t) = -0.5t² + 10t - 20. At what month does the company reach its maximum profit?

2. The population growth of a city is modeled by an exponential function. If the initial population was 100,000 and it doubled in 20 years, which graph would best represent this growth?

3. The   of a graph represents the rate of change between two variables.

4. A graph showing the relationship between distance and time for an object moving at a constant speed would be a   line.

5. A scientist is tracking the decay of a radioactive substance. The half-life is 5 years. If she starts with 100 grams, sketch a graph showing the amount of substance remaining over 20 years. Label your axes.

6. Explain how the slope of a velocity-time graph can be used to determine the acceleration of an object.

7. The bar graph below shows the number of cars sold by a dealership over five months.

a) In which month did the dealership sell the most cars?  

b) What was the total number of cars sold in the first three months?  

c) What is the difference in car sales between May and March?  

8. A scatter plot with a strong positive correlation implies that an increase in one variable causes an increase in the other.

9. A biologist is studying a bacterial colony that initially has 500 cells. The colony triples every hour. Write an equation to model this growth and then describe what the graph of this function would look like. Include key features such as intercepts, asymptotes, and the general shape.