\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
You deposit \(\dollar\)1000 in a savings account that earns 5\(\pourcent\) compound interest per year. Compound interest means that each year, interest is calculated on the current balance (principal plus any previously earned interest), and added to the balance.
Let \(u_n\) be the amount in the account after \(n\) years.
  1. What are the first three terms of the sequence \((u_n)\)?
    • \(u_1 =\)
      dollars
    • \(u_2 =\)
      dollars
    • \(u_3 =\)
      dollars
  2. What is its recursive rule?
    \(u_{n+1}=\)
  3. What is its explicit rule?
    \(u_{n}=\)
  4. How many dollars will be in the account after 10 years? (Round to two decimal places if necessary.)
    \(u_{10}=\)
    dollars