Question

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

f(t) = 1.1t2 - 2.5t + 1.5

The average rate of change of f(t) from t = 3 to t = 5 is ______ thousand owners per year.

Answer 1

9.9 - 7.5 + 1.5 =3.9

Answer 2

So are you sure about that? =) @godmod360

Answer 3

considering he only substituted in t=3 he has no idea what he is doing

Answer 4

Okay so how would u propose doing it, @amorfide =)

Answer 5

the question mentions rate of change, therefore we will differentiate f(t)

then you would substitute t=5, t=3
and subtract the answers

Answer 6

1.1(3)^2 -2.5(3) +1.5 = the t=3 answer right?

Answer 7

http://prntscr.com/6fy2he or you can use that formula

Answer 8

and then 1.1(5)^2 -2.5(5) + 1.5 = the t=5 answer?

Answer 9

\[\frac{ f(3+2)-f(3) }{ 2 }\]

Answer 10

you mean, 3 +5?

Answer 11

oh wait nvr mind =)
So i have my two answers: 3.9 and 16.5 =)

Answer 12

no
3 represents the starting x value
and the triangle x means the change in x from 3 to 5

so 2=triangle x

Answer 13

okay that's fine, u r starting to confuse me =) lol

Answer 14

sorry, I should have mentioned it in terms of t lol

Answer 15

lol okay =)

Answer 16

So. . . . . . .? is it 12.6?

Answer 17

the original expression for a derivative of a function is

\[f'(t)=\frac{ f(t _{0} + (t _{1}-t _{0})) - f(t _{0}) }{ t _{1}-t _{0} }\]


t0 is the starting t value t=3
t1 is ending t value t=5

rate of change means you want to see how the gradient function also known as the differential function changes

Answer 18

there you go got there in the end

Answer 19

so the answer is

Answer 20

12.6/2

Answer 21

6.3

Answer 22

okay awesome thx =)

Answer 23

sorry for taking so long

Answer 24

lol it's okay =) thx anyway