The table below represents the volume of a liquid sample as a function of its temperature:
Temp (C) Volume (ml)
x f(x)
11 95
16 100
21 105
26 110
The average rate of change of f(x) between x=11 to x=21 is _____ ml per C ((degrees)) and represents the rate of change of volume per degree rise in temperature
I keep getting 5 but im not sure please help :(
100
It would help if you showed your work. How do you get 5?
x is °C
f(x) is ml, so
the rate of change of ml/°C is just Δf/Δx = 5/5 = 1
For problems like this, you must read the question carefully to see just what they are asking. You gave the quantity of change (no idea whether you meant x of f(x)), but they asked for the rate of change.
To find the average rate of change of f(x) between x=11 to x=21, we need to calculate the difference in volume divided by the difference in temperature.
Let's start by finding the difference in volume:
f(21) - f(11) = 105 - 95 = 10 ml
Next, let's find the difference in temperature:
21 - 11 = 10 C
Now, we can calculate the average rate of change:
Average Rate of Change = (Difference in Volume) / (Difference in Temperature)
= 10 ml / 10 C
= 1 ml/C
Therefore, the average rate of change of f(x) between x=11 to x=21 is 1 ml per C (degree), which represents the rate of change of volume per degree rise in temperature.
To find the average rate of change of f(x) between x=11 and x=21, we need to calculate the change in volume (Δvolume) divided by the change in temperature (Δtemperature).
The change in volume is calculated by subtracting the initial value from the final value: Δvolume = f(21) - f(11) = 105 ml - 95 ml = 10 ml.
The change in temperature is simply the difference between the final and initial temperatures: Δtemperature = 21°C - 11°C = 10°C.
Now, we can find the average rate of change by dividing Δvolume by Δtemperature: average rate of change = Δvolume / Δtemperature = 10 ml / 10°C = 1 ml/C.
Therefore, the average rate of change of f(x) between x=11 and x=21 is 1 ml per degree Celsius, which represents the rate of change of volume per degree rise in temperature.