Final answer:
To represent Iris's checking account interest with a linear function, we use the simple interest formula f(t) = P × r × t, where P is the principal amount ($190), r is the annual interest rate as a decimal (0.05), and t is the time in years. This yields the function f(t) = 190 × 0.05 × t.
Step-by-step explanation:
To write a linear function representing the interest Iris's checking account accumulates, we practice using the simple interest formula. The formula to calculate simple interest is:
I = P × r × t
Where I represents the interest, P is the principal amount (initial amount of money), r is the interest rate (as a decimal), and t is the time in years.
For Iris's account, the principal P is $190, and the annual interest rate r is 5%, which we convert to a decimal by dividing by 100, resulting in 0.05. The linear function f(t) = P × r × t represents the total interest Iris earns after t years. Therefore, the function is:
f(t) = 190 × 0.05 × t
This function can be used to calculate the interest for any number of years. For example:
- After 1 year: f(1) = 190 × 0.05 × 1 = $9.50
- After 3 years: f(3) = 190 × 0.05 × 3 = $28.50