Question

Let f(x)=x^2. On the interval [2,3], the value of f increases by...

A. 2%

B. 3%

C. 125%

D. it doubles

***I don't remember how to do this at all :( Can you please explain it to me step by step? Thank you so much!! :)

Answer 1

Find f(2) and f(3). What do you get?

Then you need to find a percent change.

\(percent~change = \dfrac{new~value - old~value}{old~value} \times 100\)

For this problem, new falue is f(3), and old value is f(2).

Answer 2

okay, so f(2)=4 and f(3)=9 right?

Answer 3

but what would the new value be? :/ do i use f(2) or f(3) ?

Answer 4

or am I doing f(3)-f(2)/f(2) ? :/

Answer 5

You're changing from 2 (old) to 3 (new), so \(\%=\dfrac{f(3)-f(2)}{f(2)}\).

Answer 6

times 100...

Answer 7

okay so it's 9-4/4=5/4x100=500/4=125

so my answer is C. 125% ?? :O

Answer 8

Yes, correct. 125% sounds like a lot, but it's really just multiplying 2 by 125/100 = 5/4

Answer 9

okay, awesome!!:) thank you!! so whenever there's a problem that speaks of interval, i'm just applying both of those numbers to f(x) and then the first number is the new and the second is old? and i just apply it to the percentage change equation?

Answer 10

f(3) = 9
f(2) = 4
% change = ((9 - 4)/4)*100 = 125%
You are correct.

Answer 11

hehe yay thanks you guys!! :)

Answer 12

wlcm