Table of contents |
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Derivatives in Everyday Scenarios |
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Practice Problems: Interpreting Derivatives |
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Solutions to Practice Problems |
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Conclusion |
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Congratulations on mastering the art of calculating derivatives! Now, let’s explore how these mathematical tools apply to real-life scenarios in Unit 4.
Question 1: Ant Farm Growth
Michael has an ant farm. The function A(t) gives the amount of ants on the farm after t days. What is the best interpretation A′(5)=12?
(A) After 5 hours, the ant farm grows by 12 ants per hour.
(B) After 12 days, the ant farm grows by 5 ants per day.
(C) After 5 days, the ant farm grows by 12 ants per day.
(D) After 5 days, the ant farm shrinks by 12 ants per day.
Question 2: Instagram Followers
Anna runs an Instagram account, and F(t) represents her follower count after t months. What does F'(2) = -300 mean?
(A) After 2 months, Anna’s account loses 300 followers per month.
(B) After 2 months, Anna’s account gains 300 followers per month.
(C) After 2 weeks, Anna’s account loses 300 followers per week.
(D) After 2 weeks, Anna’s account gains 300 followers per week.
Question 3: Business Earnings
Daniel operates a business, and P(t) represents the business’s earnings in dollars after t days. What does P'(3) = 200 mean?
(A) After 3 months, the business loses 200 dollars per month.
(B) After 3 days, the business earns 200 dollars per day.
(C) After 3 days, the business has earned 200 dollars total.
(D) After 3 days, the business has lost 200 dollars.
Solution to Question 2
F(t) represents Anna’s follower count after t months, so F'(t) is the rate of change in followers (in followers per month). A negative derivative, F'(2) = -300, indicates a loss of followers. Thus, it means Anna’s account is losing 300 followers per month after 2 months.
Correct Answer: A) After 2 months, Anna’s account loses 300 followers per month.
Solution to Question 3
P(t) represents the business’s earnings in dollars after t days, so P'(t) is the rate of change in earnings (in dollars per day). Thus, P'(3) = 200 means the business is earning 200 dollars per day after 3 days.
Correct Answer: B) After 3 days, the business earns 200 dollars per day.
26 videos|75 docs|38 tests
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1. What is the derivative used for in everyday scenarios? | ![]() |
2. How can I interpret the meaning of a derivative in real life? | ![]() |
3. What are some common examples of derivatives in daily life? | ![]() |
4. How do derivatives help in making informed decisions? | ![]() |
5. What is the significance of understanding derivatives for students? | ![]() |