Edexcel Mathematics Sample paper · Paper 1 · Question 6 · ExamRizz

ExamRizzEdexcel MathematicsMathematics

Sample paper · Paper 1 · Question 6 · 7 marks

6. A company plans to extract oil from an oil field. The daily volume of oil V, measured in barrels that the company will extract from this oil field depends upon the time, t years, after the start of drilling. The company decides to use a model to estimate the daily volume of oil that will be extracted. The model includes the following assumptions: • The initial daily volume of oil extracted from the oil field will be 16 000 barrels. • The daily volume of oil that will be extracted exactly 4 years after the start of drilling will be 9000 barrels. • The daily volume of oil extracted will decrease over time. The diagram below shows the graphs of two possible models. V V (0, 16 000) (0, 16 000) (4, 9000) (4, 9000) O t O t (a) (i) (ii) Model A Model B Use model A to estimate the daily volume of oil that will be extracted exactly 3 years after the start of drilling. Write down a limitation of using model A. (2) (b) (i) (ii) Using an exponential model and the information given in the question, find a possible equation for model B. Using your answer to (b)(i) estimate the daily volume of oil that will be extracted exactly 3 years after the start of drilling.

Lesson: Exponential Functions and Their Graphs