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A new smartphone was released by a company - Edexcel - A-Level Maths Pure - Question 9 - 2020 - Paper 1
Question 9
A new smartphone was released by a company. The company monitored the total number of phones sold, n, at time t days after the phone was released. The company obse... show full transcript
Worked Solution & Example Answer:A new smartphone was released by a company - Edexcel - A-Level Maths Pure - Question 9 - 2020 - Paper 1
Step 1
the rate of increase of n was proportional to n
Answer
Given that the rate of increase of the number of phones sold, n, is proportional to n, we can express this relationship mathematically as:
where k is a positive constant of proportionality. This equation indicates that the change in n over time t is directly proportional to the current quantity of n.
Step 2
Write down a suitable equation for n in terms of t
Answer
To derive an equation for n in terms of t, we can solve this differential equation. The general solution to this equation demonstrates that:
where A is a constant representing the initial amount of phones sold at time t = 0, and k is a positive constant.