Answer:
Step-by-step explanation:a. Change and Percentage Change from Year 1 to Year 5:
Change = Balance at Year 5 - Balance at Year 1 = $1908.80 - $1489.55 = $419.25.
Percentage Change = (Change / Balance at Year 1) * 100 = ($419.25 / $1489.55) * 100 ≈ 28.15%.
b. Average Rate of Change from Year 1 to Year 5:
Average Rate of Change = (Change / Number of Years) = ($419.25 / 4 years) = $104.81 per year.
Interpretation: On average, your balance increased by approximately $104.81 each year from the end of year 1 through the end of year 5.
c. Average Rate of Change from the Middle of Year 4 to the End of Year 4: Unfortunately, we cannot calculate this average rate of change because we don't have the data for the middle of year 4.
d. Finding a Model for the Data and Average Rate of Change over the Last Half of Year 4:
To find a model, you can use the formula A = P * e^(rt), where A is the amount, P is the principal (initial investment), e is the mathematical constant (~2.71828), r is the annual interest rate (unknown), and t is the time in years.
Use the data at year 5 ($1908.80) and the initial investment ($1400) to solve for 'r.'
Calculate 'r' to be approximately 5.13%.
With this 'r,' you can find the balance at the middle of year 4 and the end of year 4 and then calculate the average rate of change over that period.