Questions: The table shows the amount of apples sold by a fruit company in millions of pounds per year from 2010 to 2015. Compute the one-year average rates of change from 2010 to 2015. Year (t) 2010 2011 2012 2013 2014 2015 --------------------- H(t) (millions of pounds) 1.5 1.7 2 2.7 3.5 4.3 a. 2010 to 2011: b. 2011 to 2012: c. 2012 to 2013: d. 2013 to 2014: e. 2014 to 2015:

Solution Steps

The problem asks for the one-year average rates of change in the amount of apples sold (in millions of pounds) from 2010 to 2015. The average rate of change between two years is calculated as the difference in the amount of apples sold divided by the difference in years.

The average rate of change between two points \( t_1 \) and \( t_2 \) is given by: \[ \text{Average rate of change} = \frac{H(t_2) - H(t_1)}{t_2 - t_1} \] Since the time difference between consecutive years is 1, the formula simplifies to: \[ \text{Average rate of change} = H(t_2) - H(t_1) \]

Using the table:

• \( H(2010) = 1.5 \) million pounds
• \( H(2011) = 1.7 \) million pounds

The average rate of change is: \[ H(2011) - H(2010) = 1.7 - 1.5 = 0.2 \, \text{million pounds per year} \]

Using the table:

• \( H(2011) = 1.7 \) million pounds
• \( H(2012) = 2.0 \) million pounds

The average rate of change is: \[ H(2012) - H(2011) = 2.0 - 1.7 = 0.3 \, \text{million pounds per year} \]

Using the table:

• \( H(2012) = 2.0 \) million pounds
• \( H(2013) = 2.7 \) million pounds

The average rate of change is: \[ H(2013) - H(2012) = 2.7 - 2.0 = 0.7 \, \text{million pounds per year} \]

The remaining parts (d and e) are left unanswered as per the instructions.

Final Answer