Final answer:
Without the initial sum, we cannot directly calculate the interest rate using the compound interest formula; however, a graph of the function y = C(x) could be used to visually determine the growth factor and thus infer the interest rate for the final account balance of $2830.
Step-by-step explanation:
To find the interest rate (r) that the account earned when the total amount after four years is $2830, we can refer to the formula of compound interest: A = P(1 + r/n)^(nt), where A is the amount of money accumulated after n years, including interest, P is the principal amount (the initial sum of money), r is the annual interest rate (decimal), n is the number of times that interest is compounded per year, and t is the time the money is invested for in years.
In this case, because the student has not provided the initial sum of money or the number of times that interest is compounded per year, we cannot use the compound interest formula directly. However, using a graph of the function y = C(x) where C(x) represents the account balance after four years, we can compare the final amount of $2830 to the projected amounts with varying interest rates to see which growth factor corresponds to the actual account balance.
Imagine a graph where the x-axis represents the growth factor (which is directly affected by the interest rate) and the y-axis represents the total amount in the account after four years. By plotting the function and visually identifying the point at which y equals $2830, we can determine the corresponding growth factor. To find the precise interest rate that would result in a balance of $2830 after four years, without additional data, we would need access to other variables or the use of formal graphing techniques and tools.