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Part 1:
Given that a<span> store had 235 MP3 players in the month of January and that every month, 30% of the MP3 players were sold and 50 new MP3 players were stocked in the store.
</span>The number of MP3 players in the store after the previous months sale is given by 0.7f(n - 1) and <span>the number of MP3 players in the store after new MP3 were added is 0.7f(n - 1) + 50.
Therefore, the </span><span>recursive function that best represents the number of MP3 players in the store f(n) after n months is given by </span><span>f(n) = 0.7 x f(n − 1) + 50, f(0) = 235, n > 0
Part 2:
The average rate of change of a function from a to b is given by
Given that the </span><span>equation showing the value of her investment after x years is given by
Thus, </span><span>the average rate of change of the value of Sophia's investment from the second year to the fourth year is given by
Therefore, the </span><span>average rate of change of the value of Sophia's investment from the second year to the fourth year is 28.25 dollars per year.</span>
Given that a<span> store had 235 MP3 players in the month of January and that every month, 30% of the MP3 players were sold and 50 new MP3 players were stocked in the store.
</span>The number of MP3 players in the store after the previous months sale is given by 0.7f(n - 1) and <span>the number of MP3 players in the store after new MP3 were added is 0.7f(n - 1) + 50.
Therefore, the </span><span>recursive function that best represents the number of MP3 players in the store f(n) after n months is given by </span><span>f(n) = 0.7 x f(n − 1) + 50, f(0) = 235, n > 0
Part 2:
The average rate of change of a function from a to b is given by
Given that the </span><span>equation showing the value of her investment after x years is given by
Thus, </span><span>the average rate of change of the value of Sophia's investment from the second year to the fourth year is given by
Therefore, the </span><span>average rate of change of the value of Sophia's investment from the second year to the fourth year is 28.25 dollars per year.</span>