Oliwia is opening a bank account. She learns that there is a special promotion where if she deposits $3,000 and then makes no additional deposits or withdrawals, her account will earn $3 in interest per month. Write the equation of a linear function that models the relationship between number of months and total amount of money Oliwia will have in her account.(1 point)

Responses

y=1,000x+3
, where x
is the number of months and y
is the total amount of money Oliwia will have in her account.
y equals 1,000 x plus 3 , where x is the number of months and y is the total amount of money Oliwia will have in her account.

y=3x+1,000
, where x
is the number of months and y
is the total amount of money Oliwia will have in her account.
y equals 3 x plus 1,000 , where x is the number of months and y is the total amount of money Oliwia will have in her account.

y=3,000x+3
, where x
is the number of months and y
is the total amount of money Oliwia will have in her account.
y equals 3,000 x plus 3 , where x is the number of months and y is the total amount of money Oliwia will have in her account.

y=3x+3,000
, where x
is the number of months and y
is the total amount of money Oliwia will have in her account.
y equals 3 x plus 3,000 , where x is the number of months and y is the total amount of money Oliwia will have in her account.
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1 answer

To derive the equation that models the total amount of money in Oliwia's bank account over time, we start with the initial deposit amount and account for the monthly interest.

  1. Initial Deposit: Oliwia deposits $3,000.
  2. Monthly Interest: The account earns $3 in interest per month.

Let \( x \) be the number of months. The total amount of money, \( y \), in the account after \( x \) months can be expressed as:

\[ y = \text{initial deposit} + \text{(interest per month)} \times \text{(number of months)} \]

Substituting the values we have:

\[ y = 3,000 + 3x \]

Thus, the equation of the linear function that models the relationship between the number of months \( x \) and the total amount of money \( y \) in her account is:

\[ y = 3x + 3,000 \]

So the correct response is:

y = 3x + 3,000, where x is the number of months and y is the total amount of money Oliwia will have in her account.