Question

Molly is comparing savings account options at 2 banks. Let x represent the number of years the money is in the bank.Bank A provides Molly the equation f(x)=3x^2-2x+5 to model an account’s growth. Bank B provides molly the equation f(x)=1.5^x-1 to model the account’s growth. The table below illustrates the growth for each account in 5-year intervals. Which statement describes the account options?-Bank A’s account balance will always exceed Bank B’s account balance-Bank A’s account balance will exceed Bank B’s account balance between 15 and 20 years-Bank B’s account balance will always exceed Bank A’s account balance-Bank B’s account balance will exceed Bank A’s account balance between 15 and 20 years

Answer 1

To solve this question, let's compare the account balances for each time.

x = 5

Bank A - f(5) = 70

Bank B - f(5) = 6.59

Bank A f(5) > Bank B f(5)

x = 10

Bank A - f(10) = 285

Bank B - f(10) = 56.67

Bank A f(10) > Bank B f(10)

x = 15

Bank A - f(15) = 650

Bank B - f(15) = 436.89

Bank A f(15) > Bank B f(15)

x = 20

Bank A - f(20) = 1165

Bank B - f(20) = 3324.26

Bank A f(20) < Bank B f(20)

If when x = 0, 5, 10, and 15 The account balance for Bank A was greater and when x = 20 the account balance for Bank B was greater, then Bank B’s account balance will exceed Bank A’s account balance between 15 and 20 years.

Answer: Bank B’s account balance will exceed Bank A’s account balance between 15 and 20 years.