Question

Bryan has a prepaid cell phone with a balance of $52
. He is charged the same rate per minute.

• After 1
minute, his balance is $45
.
• After 2
minutes, his balance is $38
.
• After 3
minutes, his balance is $31
.

Complete the equation that represents the balance on the phone after n
minutes.

Answer 1

Use your function to find the number of minutes it takes Bryan to reach a balance of $0.

Round your answer to the nearest minute.

Answer 2

To find the equation that represents Bryan's balance after \( n \) minutes, we first need to determine the rate at which his balance decreases per minute.

Let's analyze the information provided:

- After 1 minute, his balance is $45.
- After 2 minutes, his balance is $38.
- After 3 minutes, his balance is $31.

From this, we can see how much his balance decreases each minute:

- From minute 0 to minute 1: \( 52 - 45 = 7 \) (balance decreased by $7)
- From minute 1 to minute 2: \( 45 - 38 = 7 \) (balance decreased by $7)
- From minute 2 to minute 3: \( 38 - 31 = 7 \) (balance decreased by $7)

This shows that Bryan is charged $7 per minute.

Now, we write the equation to represent the balance after \( n \) minutes.

The total balance can be calculated as:

\[
\text{Balance} = \text{Initial Balance} - (\text{Charge per minute} \times n)
\]

Given:
- Initial balance = $52
- Charge per minute = $7

Thus, the equation for the balance \( B \) after \( n \) minutes is:

\[
B = 52 - 7n
\]

So the completed equation is:

\[
B = 52 - 7n
\]

Answer 3

To find the number of minutes it takes for Bryan to reach a balance of $0 using the function we derived, we set the balance \( B \) to 0 in the equation:

\[
B = 52 - 7n
\]

Setting \( B = 0 \):

\[
0 = 52 - 7n
\]

Now, solve for \( n \):

\[
7n = 52
\]

\[
n = \frac{52}{7} \approx 7.4286
\]

Rounding to the nearest minute, we find:

\[
n \approx 7
\]

Thus, it takes Bryan approximately **7 minutes** to reach a balance of $0.