13. you budget $100 for parking each month. each day you use the downtown
parking lot, it costs you $5. write a rule to represent the amount of money left in
your monthly budget as an arithmetic sequence. how much money is left in your
budget after you have used the downtown parking lot 11 times this month?

t = 100 - 5n : rule for amount of money left.

You will have $45 left after using downtown parking 11 times.

Explanation:

The equation for an arithmetic sequence in this case is t = a + dn.

a is the initial value, d is the rate of change, and n is the independent variable.

t is the dependent variable.

In this context, a is the starting budget for parking, d is the amount parking costs each time, n is the number of times you use the parking and t is the amount of money left after each time you use the parking.

Substitute the known values from the problem into the equation.

t = a + dn

t = 100 + (-5)n   <= the rate of change is -5 because it's decreasing

t = 100 - 5n

To find the amount of money left after 11 times using downtown parking, substitute n for 11.

t = 100 - 5n

t = 100 - 5(11)

t = 100 - 55

t = 45

You will have $45 left after 11 times parking downtown.