Answer:
Explained below.
Step-by-step explanation:
At the start of every month the price of gas started out at 100¢/gallon.
Then every day since, it has gone up 2¢/gallon.
The variables are denoted as follows:
<em>d</em> = the date
<em>g</em> = price of a gallon of gas
<em>c</em> = total price required to fill up my car, in cents.
(a)
The function that gives the price of gas on any given day of the month is:
g (d) = 100 + 2(d - 1)
The (d - 1) represent the number of times the price has gone up by 2¢/gallon.
(b)
The function that tells how much money it takes to fill up my car, as a function of the price of a gallon of gas is:
c (g) = 10 × g
Since the car takes 10 gallons of gas.
(c)
The composite function that gives the cost of filling up my car on any given day of the month is:
c (g (d)) = 10 × g (d)
= 10 [100 + 2(d - 1)]
c (g (d)) = 1000 + 20 (d - 1)
(d)
On the 11th day the price of gas has increased by 2¢/gallon for the past 10 days.
Compute the total price it takes to fill up my car on the 11th of the month as follows:
c (g (d)) = 1000 + 20 (d - 1)
c (g (11)) = 1000 + 20 (11 - 1)
= 1000 + (20 × 20)
= 1000 + 400
= 1400¢
Thus, the it takes to fill up my car on the 11th of the month is 1400¢.
(e)
The total price to fill the car on the <em>n</em>th day is 1040¢.
Compute the value of <em>n</em> as follows:
c (g (d)) = 1000 + 20 (d - 1)
1040 = 1000 + 20 (n - 1)
1040 - 1000 = 20 (n - 1)
40 = 20 (n - 1)
(n - 1) = 2
n = 3
Thus, the day on which it cost 1,040¢ to fill up the car is the 3rd day.
