Question

In: Advanced Math

In the UK sales of music CDs per year have declined from 60 million in 2013...

  1. In the UK sales of music CDs per year have declined from 60 million in 2013 to 48 million in 2016 and further to 32 million in 2018.

    1. (a) What was the average rate of change in CD sales from 2013 to 2016 and what was the average rate of change from 2016 to 2018.

    2. (b) Based on this data, is number of CDs sales decreasing linearly? Give a reason for your answer.

  2. The cost of producing x solar panels is c(x) = 1000 + 500x − 20x2 (in dollars).

    1. (a) Using the definition of the derivative from lectures, compute the marginal cost when 10 solar panels have already been produced.

    2. (b) Compare this to the actual extra cost for producing an 11th solar panel.

    3. (c) Work out the equation for the tangent to the graph of c(x) at x = 10.


Calculus
1. In the UK sales of music CDs per year have declined from 60 million in 2013 to 48 million in 2016 and further to 32 million in 2018.
(a) What was the average rate of change in CD sales from 2013 to 2016 and what was the average rate of change from 2016 to 2018.
(b) Based on this data, is number of CDs sales decreasing linearly? Give a reason for your answer.
2. The cost of producing x solar panels is c(x) = 1000 + 500x − 20x^2 (in dollars).
(a) Using the definition of the derivative from lectures, compute the marginal cost when 10 solar panels have already been produced.
(b) Compare this to the actual extra cost for producing an 11th solar panel.
(c) Work out the equation for the tangent to the graph of c(x) at x = 10.

Calculus
1. In the UK sales of music CDs per year have declined from 60 million in 2013 to 48 million in 2016 and further to 32 million in 2018.
(a) What was the average rate of change in CD sales from 2013 to 2016 and what was the average rate of change from 2016 to 2018.
(b) Based on this data, is number of CDs sales decreasing linearly? Give a reason for your answer.
2. The cost of producing x solar panels is c(x) = 1000 + 500x − 20x^2 (in dollars).
(a) Using the definition of the derivative from lectures, compute the marginal cost when 10 solar panels have already been produced.
(b) Compare this to the actual extra cost for producing an 11th solar panel.
(c) Work out the equation for the tangent to the graph of c(x) at x = 10.

Solutions

Expert Solution

Colby Messinger answered 1 year ago
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