The table below shows the cost of renting a bike for a given amount of time, find the rate of change in cost with respect to time.

Table: Time: 1.75, 4, 7.
Cost( Dollars)4.375, 10, 17.5

Could one of the tutors please explain to me how to this?

Thanks :)

-Allyson

first, find the "velocity function"

cost/time: 4.375/1.75; 10/4; 17.5/7

cost/time: 2.5; 2.5; 2.528 $/hr

Well, the rate of change between the first increment and the second is zero.
The rate of change for the second to last increment is (2.528-2.5)/(7-4)=.00933 $/hr/hr

To find the rate of change in cost with respect to time, we need to calculate the slope of the cost-time relationship. In other words, we need to find how much the cost changes for each unit increase in time.

To do this, we can look at the two points on the table: (1.75, 4.375) and (4, 10). We will use these two points to calculate the slope.

The slope formula is given by:
slope = (change in y)/(change in x)

In this case, y represents the cost, and x represents the time.

Let's calculate the change in y and change in x:

Change in y = 10 - 4.375 = 5.625
Change in x = 4 - 1.75 = 2.25

Now, we can calculate the slope:
slope = (change in y)/(change in x) = 5.625/2.25 = 2.5

Therefore, the rate of change in cost with respect to time is 2.5. This means that for every unit increase in time, the cost of renting a bike increases by $2.5.

I hope this explanation helps! Let me know if you have any further questions.