Question

Diane owes $30201.00 to the bank after completing her college degree. With the funds from her new job she is paying back $204.00 per month. Her friend Teresa was given $6476.50 in the bank for college from her family, and she is spending $221.00 per month out of this college fund. If these were continuous functions, after how many months will Diane have the same bank balance than Teresa, rounded to the nearest tenth?

Answer 1

Diane and Teresa will have the same bank balance after approximately 345.7 months, calculated by setting up an equation representing each person's bank balance over time and solving for when they are equal.

Step-by-step explanation:

To find out after how many months Diane and Teresa will have the same bank balance, we need to create two equations that represent their respective balances over time and then solve for when the balances are equal.

Diane's balance over time is modelled by the equation:
BD(t) = -30201 + 204t, where t is the number of months.
Here, Diane starts with a negative balance because she owes money, and with each passing month (t), her balance increases by $204 as she pays off the debt.

Similarly, for Teresa, who is spending from her college fund, we have:
BT(t) = 6476.50 - 221t.

To find the month when their balances are equal, we set the equations equal to each other and solve for t:
-30201 + 204t = 6476.50 - 221t
425t = 30201 + 6476.50
t = (30201 + 6476.5) / 425
t = 345.67 or approximately 345.7 months.

Diane would therefore have the same bank balance as Teresa after about 345.7 months, rounded to the nearest tenth.