Choose the function whose graph is given by:
2 answers:
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Answer:
Part a) Your budget is $40.
Part b) The price for one gallon of gasoline is $3.55, while a car wash costs $8.
Part c)
Part d) Refer to the explanation below.
Step-by-step explanation:
Please see the complete question in the attached image.
Part a) The budget is expressed by the equation
y = 40
therefore,
Your budget amounts to $40.
Part b) In terms of costs, how much is a gallon of gasoline and what is the car wash price?
Let
y ------> denote the total cost for a gallon of gasoline along with a car wash
x -----> define the volume of gasoline in gallons
We can express the relationship as
y = 3.55x + 8
For calculations, when x = 0, we have:
y = 3.55(0) + 8 = 8
The y-intercept signifies the cost of the car wash, being $8.
Now, to identify the price of one gallon of gasoline:
We know the slope of the linear function is
m = $3.55 per gallon
This confirms that a gallon of gasoline costs $3.55.
Part c) Formulate an inequality representing the potential quantity of gasoline you can purchase:
We have:
Now, solve for x:
Part d) Utilize the graph to determine the solution of the inequality from part c)
We can set up the system:
y = 40
y = 3.55x + 8
The solution lies at the intersection of both graphs. By observing the graph, the intersection appears to be around (9, 40).
This indicates that the maximum volume of gasoline purchasable within your budget is approximately 9 gallons.
Response:
$3,000
Detailed breakdown:
This scenario is centered around compound interest, with the formula for compound interest defined as
Provided Data
A = final amount =?
P = initial principal balance = $2,500
r = interest rate = 2.1%= 0.021
t = number of time units passed= 14 years
By inserting our data into the compound interest equation, we can determine the final amount
Therefore, rounding to the nearest hundred gives us an account balance of $3,000