It appears that the imports of carbon black have been increasing by about 10% annually. year - imports of carbon black (thousands of tons) 2010 - 92.0 2011 - 101.0 2012 - 112.0 2013 - 124.0 2014 - 135.0 2015 - 149.0 2016 - 163.0 2017 - 180.0 1. determine the logarithmic trend equation.2. by what percent did imports increase, on the average, during the period? (round your answer to 2 decimal places.)3. estimate imports for the year 2017. (round your answer to 2 decimal places.)

a) For this case we want to find an equation on the following form:

And if we use excel as we can see on the figure attached the best model is:

b) For this case we can use the relative change in order to calculate the % of variation between 2010 and 2017:

c) If we use the model created we just need to replace x =8 and we got:

And the difference respect the observed values is:

Explanation:

For this case we have the following data, let X= the amount of years since 2009. Because if we select starting from 0 the natural log of 0 not exists.

t             x         y

2010      1       92.0

2011       2        101.0

2012      3       112.0

2013      4       124.0

2014      5       135.0

2015      6       149.0

2016      7       163.0

2017       8       180.0

Part a

For this case we want to find an equation on the following form:

And if we use excel as we can see on the figure attached the best model is:

Part b

For this case we can use the relative change in order to calculate the % of variation between 2010 and 2017:

Part c

If we use the model created we just need to replace x =8 and we got:

And the difference respect the observed values is: