Ben wants to buy a new car, and she has narrowed her choices to two models.
Model A sells for $12,500, gets 25mi/gal, and costs $300 a year for insurance
Model B sells for $16,100, gets 36 mi/gal, and costs $400 a year for insurance.
Jenny drives about 36,000 miles a year, and gas costs about $3 a gallon.
a. Find a formula for the total cost of owing Model A for any number of years.
b. Find a formula for the total cost of owing Model B for any number of years.
c. Make a table of the total cost of owning each model from 1 year to 6 years, in 1 year increments.
d. If Ben expects to keep the car for 2 years, which model is more economical?
e. What do you suppose is causing this trend?
Please help!!!!
I'll get you started with A. Its cost for n years is
A(n) = 12500 + 300n + 3(36000/25)n
do the same with B, changing the numbers as needed.
Then you can make the table and compare costs for 2 years.
So for part B would it be:
A(n)=16100+400n+3(36000/36)n
For part D do we substitute the 2 in with "n"?
Can you help me with part e please?
a. To find the total cost of owning Model A for any number of years, we need to consider the cost of the car, insurance, and fuel. Let's denote the number of years as 'n'.
The cost of the car, Model A, is $12,500.
The cost of insurance for each year is $300.
The cost of fuel can be calculated by multiplying the number of miles driven per year (36,000) by the cost per gallon ($3) and dividing it by the mileage of the car (25 miles/gallon):
Fuel cost per year = (36,000 miles/year * $3/gallon) / 25 miles/gallon
To find the total cost of owning Model A for 'n' years, we can use the following formula:
Total cost Model A = Cost of the car + (Insurance cost per year * n) + (Fuel cost per year * n)
b. Similarly, to find the total cost of owning Model B for any number of years, we use the same formula but with the respective values for Model B:
The cost of the car, Model B, is $16,100.
The cost of insurance for each year is $400.
The fuel cost per year for Model B can be calculated in the same way:
Fuel cost per year = (36,000 miles/year * $3/gallon) / 36 miles/gallon
Total cost Model B = Cost of the car + (Insurance cost per year * n) + (Fuel cost per year * n)
c. To make a table of the total cost of owning each model from 1 to 6 years, we can substitute the values into the formulas for both models and calculate them. Here's an example table:
| Years | Total cost Model A | Total cost Model B |
|-------|-------------------|-------------------|
| 1 | Formula result 1 | Formula result 1 |
| 2 | Formula result 2 | Formula result 2 |
| 3 | Formula result 3 | Formula result 3 |
| 4 | Formula result 4 | Formula result 4 |
| 5 | Formula result 5 | Formula result 5 |
| 6 | Formula result 6 | Formula result 6 |
d. If Ben expects to keep the car for 2 years, we can calculate the total cost for both models using the formulas from part a and b. Then we compare the total costs of both models and choose the one with the lower cost.
e. The trend that we observe is that the cost of Model A is lower than the cost of Model B for each year. This is primarily due to the lower price of Model A and also the better fuel efficiency of Model A compared to Model B. The lower cost of insurance for Model A also contributes to the overall lower total cost.