Martina deposits the same amount of money into a bank account every month. The table below shows the amount of money in the account after different amounts of time.Time (months) 6 8 10 12Money (dollars) 467 557 647 737Answer the following questions.(a)How much money was already in the account when Martina started depositing money?dollars(b)Choose the statement that best describes how the time and the amount of money in the account are related. Then give the value requested.As time increases, the amount of money in the account decreases.At what rate is the amount of money in the account decreasing?dollarspermonthAs time increases, the amount of money in the account increases.At what rate is the amount of money in the account increasing?dollarspermonth
Question
Martina deposits the same amount of money into a bank account every month. The table below shows the amount of money in the account after different amounts of time.Time (months) 6 8 10 12Money (dollars) 467 557 647 737Answer the following questions.(a)How much money was already in the account when Martina started depositing money?dollars(b)Choose the statement that best describes how the time and the amount of money in the account are related. Then give the value requested.As time increases, the amount of money in the account decreases.At what rate is the amount of money in the account decreasing?dollarspermonthAs time increases, the amount of money in the account increases.At what rate is the amount of money in the account increasing?dollarspermonth
Solution
(a) To find out how much money was already in the account when Martina started depositing money, we need to determine the rate at which the account balance is increasing.
Looking at the table, we can see that every two months, the account balance increases by 45 (90 ÷ 2 = 45) into the account.
So, to find out the initial balance, we subtract the deposits Martina made in the first six months from the balance at that time. This means we subtract six times the monthly deposit from the balance after six months: 467 - 6*45 = $197.
So, Martina had $197 in the account when she started depositing money.
(b) As time increases, the amount of money in the account increases. The rate at which the amount of money in the account is increasing is $45 per month.
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