Question

​Iris's checking account pays simple interest at ​4% per year. She has ​$180 in her account. Write a linear function to model the amount of money in her checking account at any time t.

​A(t)=

Answer 1

The linear function to model the amount of money in Iris's checking account is A(t) = $180 + $7.20t, using the simple interest formula, which takes into account the principal amount, rate of interest, and time.

Step-by-step explanation:

To determine the linear function that models the amount of money in Iris's checking account at any time t, we use the simple interest formula: Interest = Principal × Rate × Time.

In this case, the Principal amount is $180, the Rate is 4% per year (or 0.04 expressed as a decimal), and Time is represented by t in years.

The interest earned after time t can be calculated using the formula:
I(t) = $180 × 0.04 × t.

However, we want the total amount in the account, which includes the initial principal plus the interest earned over time. The linear function representing this is:
A(t) = Principal + InterestA(t) = $180 + ($180 × 0.04 × t)

Simplifying that, we get:

A(t) = $180 + $7.20t

This function shows that for each year t, Iris earns an additional $7.20 on top of the initial $180 in her checking account.

Answer 2

The amount of money in Iris's checking account can be modeled by a linear function of the form:

y = mt + b

where y is the amount of money in the account, t is the time (measured in years), m is the rate of interest, and b is the initial amount in the account.

In this case, we have m = 0.04 (since the interest rate is 4% per year) and b = 180 (since that's the initial amount in the account). Therefore, the linear function that models the amount of money in Iris's checking account at any time t is:

y = 0.04t + 180

For example, if t = 5 (years), then the amount of money in Iris's checking account is 0.04 * 5 + 180 = 198 dollars.