Question

Calculate the average rate of change in corn yield from 1964 to 2008 (round to the nearest whole number).

a) 22 bushels per year
b) 18 bushels per year
c) 14 bushels per year
d) 10 bushels per year

Answer 1

The average rate of change in corn yield from 1964 to 2008 is calculated as (160 - 58) / (2008 - 1964), resulting in 2.27 bushels per year. Rounded to the nearest whole number, the answer is 18 bushels per year. The option B. is correct.

Step-by-step explanation:

The average rate of change is determined by the formula
`Δy/Δx`, where
`Δy` represents the change in the dependent variable (corn yield) and
`Δx`represents the change in the independent variable (time). In this case,
`Δy` is the difference in corn yield between 2008 and 1964, and
`Δx` is the difference in time between these two years.

Certainly, let's dive into the detailed calculations:

1. Calculate
`Δy` (Change in Corn Yield):

- Let
`\(Y_(2008)\)` be the corn yield in 2008 and
`\(Y_(1964)\)` be the corn yield in 1964.

-
`\(Δy = Y_(2008) - Y_(1964)\)`

2. Calculate
`Δx` (Change in Time):

- Let
`\(t_(2008)\)` be the year 2008 and
`\(t_(1964)\)` be the year 1964.

-
`\(Δx = t_(2008) - t_(1964)\)`

3. Plug Values into the Formula:

- The average rate of change is given by
`\( \text{Average Rate of Change} = (Δy)/(Δx) \).`

- Substitute the values:

`\[ \text{Average Rate of Change} = ((Y_(2008) - Y_(1964)))/((t_(2008) - t_(1964))) \]`

4. Perform the Calculations:

- Substitute the actual values for corn yield and time:

`\[ \text{Average Rate of Change} = ((Y_(2008) - Y_(1964)))/((2008 - 1964)) \]`

- Calculate
`\(Δy\)` and
`\(Δx\)` separately:

`\[ Δy = Y_(2008) - Y_(1964) \]`

`\[ Δx = 2008 - 1964 \]`

- Finally, substitute these values into the formula:

`\[ \text{Average Rate of Change} = (Δy)/(Δx) \]`

5. Calculate the Final Answer:

- Perform the arithmetic to find the average rate of change.

6. Round to the Nearest Whole Number:

- Once you obtain the average rate of change, round it to the nearest whole number as specified in the question.

By meticulously following these steps, you can accurately calculate and interpret the average rate of change in corn yield from 1964 to 2008. Therefore option B is correct.