Question

The number of students enrolled in a new course as a function of time can be represented by the function.

f(x) = (4)^x − 1

What is the average increase in the number of students enrolled per hour between hours 2 and 4?

Enter your answer in the box.

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Answer 1

@Vocaloid

Answer 2

First you'll plug 2 and 4 for x to find f(x) and then you'll find the rate of change

Answer 3

f(2) = 4^2 - 1
Can you simplify 4^2 - 1?

Answer 4

it is 15

Answer 5

Correct so when x = 2, f(x) = 15

Now for x = 4
f(4) = 4^4 - 1
Could you simplify that

Answer 6

255

Answer 7

Correct
Now the average is
\(\bf\dfrac{f(4)-f(2)}{4-2}=\dfrac{255-15}{4-2}=?\)

Answer 8

120

Answer 9

So 120 is your answer

Answer 10

ok thx for that and could you help me with other questions if you have the time if it's ok with u?

Answer 11

Sure

Answer 12

ok hold on

Answer 13

Drag and drop the answer into the box to identify each function as linear, exponential, or neither.


linear

exponential

neither

Answer 14

i'll send the pic

Answer 15

You'd have to find the rate of change
Know how to?

Answer 16

well i think i have it

Answer 17

the first is exponential

the second is linear

correct me

Answer 18

I think you have it backwards lol
For the first one it's a constant rate of 1.5 which is \(\bf linear\)
And then for the second one, it seems like it's 2^x, so 2^0 = 1, 2^3 = 8, 2^6 = 64 which makes it \(\bf exponential\)

Answer 19

oh so i had but it's backwards

Answer 20

Yep

Answer 21

i'll send the pic

Answer 22

Function f is an exponential function.

By what factor does the output value increase as each input value increases by 1?



Enter your answer in the box.

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Answer 23

Any idea?

Answer 24

no

Answer 25

do you ?

Answer 26

I know the answer but am not sure how to explain it

Answer 27

I basically kept multiplying by 2 each time and got the same thing

Answer 28

Idk why there's an image

Answer 29

ok

Answer 30

so what is it ?

Answer 31

mehek ?