Answer:
Peter opens an account with a $600 deposit that earns 8% simple interest annually. He makes no other deposits or withdrawals.
Complete the sentences:
This situation can be modeled by a linear function that grows in interest.
Peter will earn $48 in interest each year.
Step-by-step explanation:
Simple interest is calculated as a percentage of the principal amount and does not compound over time. Therefore, the amount of interest earned each year is constant, and the growth of the account is linear.
To calculate the amount of interest earned each year, we multiply the initial deposit by the interest rate:
$600 x 0.08 = $48
Therefore, Peter will earn $48 in interest each year. After four years, he will have earned:
4 x $48 = $192
So his total balance will be:
$600 + $192 = $792
Since the growth of the account is linear, we can model it with a linear function of the form:
y = mx + b
Where y is the total balance, x is the number of years, m is the slope (or rate of growth), and b is the initial balance.
In this case, the slope is the amount of interest earned each year, which is $48, and the initial balance is $600. So the linear function that models this situation is:
y = 48x + 600