Use the table to answer the question.
Years Amount
1 $1,080
2 $1,160
3 $1,240
The table shows the amount of money in a bank account after a certain number of years. What is the initial value?
The initial value is the amount of money in the bank account after 0 years. In this case, the initial value is not given in the table, but we can determine it by looking at the pattern of the amounts in the table.
If we observe the pattern:
$1,080 (1 year)
$1,160 (2 years)
$1,240 (3 years)
We see that the amount in the bank account is increasing by $80 each year. Therefore, the initial value before any time has passed is $1,000.
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?
To find out how much money Victor owes at the beginning of January, we need to evaluate the function f(x) at x = 0 (which represents the month of January).
Given f(x) = -35x + 2,500, substitute x = 0 into the function:
f(0) = -35(0) + 2,500
f(0) = 0 + 2,500
f(0) = 2,500
Therefore, Victor owes $2,500 at the beginning of January.
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?
In the given function, f(x) = 10x + 15, x represents the number of hours Cesar rents the bicycle, and f(x) represents the total cost of the rental, including the flat rate and the hourly fee.
The flat rate is the component of the total cost that does not depend on the number of hours rented. In this case, it is the constant term in the function f(x). In the function f(x) = 10x + 15, the constant term is 15.
Therefore, the flat rate for Cesar's bicycle rental is $15.