Final answer:
The interest earned in the 6th year is calculated by finding the difference in the accumulated values at the end of the 5th and 6th years using the accumulation function and multiplying this by the initial deposit of \$470.
Step-by-step explanation:
Mark wants to find out the amount of interest earned in the 6th year after depositing \$470 into a savings account with an accumulation function a(t) = 0.04t² + 0.01t + 1. To calculate the interest earned during just the 6th year, we need to evaluate the accumulation function at t=6 and t=5 to find the total account balance at the beginning and end of the 6th year, and then subtract the balance at the beginning of the year from the balance at the end of the year.
First, find the accumulated value at the end of the 5th year: a(5) = 0.04(5)² + 0.01(5) + 1.
Second, find the accumulated value at the end of the 6th year: a(6) = 0.04(6)² + 0.01(6) + 1.
The interest earned in the 6th year is the difference between these two values. Multiply this interest earned by the initial deposit of \$470 to find the amount of interest accrued during the 6th year.