Question

Use the table to answer the question.

years:
1
2
3

Amount:
$1,080
$1,160
$1,240

The table shows the amount of money in a bank account after a certain number of years. What is the initial value?

Answer 1

Victor will start paying off his credit card in January. He uses the function f(x)=−35x+2,500
to model the amount of money he owes x
months after January. How much money does he owe at the beginning of January?

Answer 2

Cesar rents a bicycle for a flat rate plus $10 per hour. He models the cost of the rental with the function f(x)=10x+15
, where x
is the number of hours he rents the bicycle, and f(x)
is the total cost of the bicycle rental, including the flat rate and the hourly fee. What is the flat rate for the bicycle rental?

Answer 3

To determine the initial value in the bank account, we can look at the increments in the amount over the years provided in the table.

From the table:

- After 1 year, the amount is $1,080.
- After 2 years, the amount is $1,160.
- After 3 years, the amount is $1,240.

Let's calculate the increase in each year:

1. From Year 1 to Year 2:
\[
1,160 - 1,080 = 80
\]

2. From Year 2 to Year 3:
\[
1,240 - 1,160 = 80
\]

We see that the account increases by $80 each year.

To find the initial value (the amount at Year 0), we can subtract the yearly increase from the Year 1 amount:

\[
\text{Initial value} = \text{Amount after 1 year} - \text{Increase} = 1,080 - 80 = 1,000
\]

Thus, the initial value in the bank account was **$1,000**.

Answer 4

To find out how much money Victor owes at the beginning of January, we need to evaluate the function \( f(x) = -35x + 2500 \) at \( x = 0 \), since January will correspond to \( x = 0 \).

Substituting \( x = 0 \) into the function:

\[
f(0) = -35(0) + 2500
\]

This simplifies to:

\[
f(0) = 0 + 2500 = 2500
\]

So, Victor owes **$2,500** at the beginning of January.

Answer 5

In the function \( f(x) = 10x + 15 \), the term \( 10x \) represents the hourly fee for renting the bicycle, where \( x \) is the number of hours rented (at $10 per hour). The constant term \( 15 \) represents the flat rate.

Therefore, the flat rate for the bicycle rental is **$15**.