Question

If you rent a car for one day and drive 225 miles, the cost is $80. If you drive 350 miles in one day, the cost is $105. Let cm) represent the cost, in dollars, of driving m miles: a) Find a linear function C(m) that fits the data. b) Use the function of part (a) to find how much it will cost to rent a car for one day and drive it 475 miles. Also, find the number of miles you can drive for $155.

Answer 1

Answer:

a) $(x_1 = 225, y_1 = 80) , (x_2 = 350, y_2 = 105)$

And we want to find a function:

$C (m) = b_1 m + b_0$

We can find the slope with this formula:

$b_1= \frac{105-80}{350-225}= \frac{25}{125}=0.2$

And then we can use the point  $(x_1 = 225, y_1 = 80)$ to find the intercept $b_o$ and we got:

$80 = 0.2*225 +b_0$

$b_0 = 80-45 = 35$

So then the linear function is given by:

$C(m) = 0.2 m + 35$

b) For this case we have that m = 475 so we can replace into the function to find the cost like this:

$C(m =475) = 0.2*475 + 35 = 130$

And for the other case we have a cost of 155 and we want to find the number of miles associated so we can do this:

$155 = 0.2m + 35$

$155-35= 120 = 0.2 m$

$m= \frac{120}{0.2}= 600 mi$

Step-by-step explanation:

For this case we can define the following notation:

m= represent the miles travelled

C= represent the cost

Part a

For this case we have the following two points given:

$(x_1 = 225, y_1 = 80) , (x_2 = 350, y_2 = 105)$

And we want to find a function:

$C (m) = b_1 m + b_0$

We can find the slope with this formula:

$b_1= \frac{105-80}{350-225}= \frac{25}{125}=0.2$

And then we can use the point  $(x_1 = 225, y_1 = 80)$ to find the intercept $b_o$ and we got:

$80 = 0.2*225 +b_0$

$b_0 = 80-45 = 35$

So then the linear function is given by:

$C(m) = 0.2 m + 35$

Part b

For this case we have that m = 475 so we can replace into the function to find the cost like this:

$C(m =475) = 0.2*475 + 35 = 130$

And for the other case we have a cost of 155 and we want to find the number of miles associated so we can do this:

$155 = 0.2m + 35$

$155-35= 120 = 0.2 m$

$m= \frac{120}{0.2}= 600 mi$