Which of the following functions has a rate of change of 5?(1 point)
Responses
f(5)=300 and f(7)=290
f left parenthesis 5 right parenthesis equals 300 and f left parenthesis 7 right parenthesis equals 290
f(3)=278 and f(5)=320
f left parenthesis 3 right parenthesis equals 278 and f left parenthesis 5 right parenthesis equals 320
f(5)=225 and f(10)=250
f left parenthesis 5 right parenthesis equals 225 and f left parenthesis 10 right parenthesis equals 250
f(2)=317 and f(5)=296
None of the given functions have a rate of change of 5.
To determine which function has a rate of change of 5, we need to calculate the slope between the given points for each function. The slope is calculated by dividing the difference in the y-values by the difference in the x-values.
For the first function:
slope = (f(7) - f(5)) / (7 - 5)
= (290 - 300) / (2)
= -10 / 2
= -5
The rate of change for the first function is -5, not 5.
For the second function:
slope = (f(5) - f(3)) / (5 - 3)
= (320 - 278) / (2)
= 42 / 2
= 21
The rate of change for the second function is 21, not 5.
For the third function:
slope = (f(10) - f(5)) / (10 - 5)
= (250 - 225) / (5)
= 25 / 5
= 5
The rate of change for the third function is 5.
For the fourth function:
slope = (f(5) - f(2)) / (5 - 2)
= (296 - 317) / (3)
= -21 / 3
= -7
The rate of change for the fourth function is -7, not 5.
Therefore, the function with a rate of change of 5 is the third function, where f(5) = 225 and f(10) = 250.
To find the rate of change for a function, you can calculate the difference in the function values and divide it by the difference in the input values.
Let's go through each function and calculate the rate of change:
1) For the first function, we have f(5) = 300 and f(7) = 290.
The difference in function values is 300 - 290 = 10, and the difference in input values is 7 - 5 = 2.
Therefore, the rate of change is 10 / 2 = 5.
2) For the second function, we have f(3) = 278 and f(5) = 320.
The difference in function values is 320 - 278 = 42, and the difference in input values is 5 - 3 = 2.
Therefore, the rate of change is 42 / 2 = 21.
3) For the third function, we have f(5) = 225 and f(10) = 250.
The difference in function values is 250 - 225 = 25, and the difference in input values is 10 - 5 = 5.
Therefore, the rate of change is 25 / 5 = 5.
4) For the fourth function, we have f(2) = 317 and f(5) = 296.
The difference in function values is 296 - 317 = -21, and the difference in input values is 5 - 2 = 3.
Therefore, the rate of change is -21 / 3 = -7.
Out of the given functions, only the first and the third functions have a rate of change of 5.