Question

Algebra!!!

Answer 1

The function below shows the number of car owners f(t), in thousands, in a city in different years t:

f(t) = 0.25t2 − 0.5t + 3.5

The average rate of change of f(t) from t = 2 to t = 6 is ______ thousand owners per year.

Answer 2

@Vocaloid @futurelegend @thomaster @LynFran

Answer 3

[f(6)-f(2)]/(6-2)

Answer 4

find f(6) and f(2), then plug them into the equation

Answer 5

You need to take the derivatives.
\[f'(t) = 0.5t -5\]

Answer 6

Oh lord, I have no idea.

Answer 7

Wait, is it 2?

Answer 8

@saseal ? @Vocaloid ?

Answer 9

f(t) = 0.25t^2 − 0.5t + 3.5
f(6) = ?

Answer 10

Yea, I suppose.

Answer 11

OK.

Answer 12

@DaBest21

Answer 13

@ganeshie8 @Hero @ParthKohli @thomaster @triciaal @Michele_Laino @alekos

Answer 14

please see the procedure of @Vocaloid

Answer 15

the average rate of change is like the slope of a best fit line
slope of a line is change in y / corresponding change in x = y2 - y1
find the y value when x = 6 this is y2 find the y value when x = 2 this is y1
the change in x from 6 to 2

this is the same thing done above by @Vocaloid

Answer 16

The line isn't straight, its a quadratic curve.
\[f(t) = 0.25t ^{2} + 0.5t +3.5\]

Answer 17

oops a typo in the function should be \[f(t) = 0.25t^2-0.5t+3.5\]

Answer 18

What vocaloid found was the total change during the total period from t=2 to t=6, but the question asked for average rate of change from period t=2 to t=6.