Question

The function below shows the number of students of a school who enrolled for cooking classes. Let f(x) represent the total number of students who enrolled for the classes after x years:

f(x) = 11(1.35)x

The average rate of change in the number of students who enrolled for cooking classes from the first to the fifth year is ________students per year.

Round your answer to the nearest whole number.

Numerical Answers Expected!

Answer 1

@dan815

Answer 2

@jim_thompson5910

Answer 3

Are you able to find f(1) ?

Answer 4

Well hear me out..

Answer 5

F(1) would be 14.85 right? because 11(1.35)^1 equals 14.85... soooo if it was 11(1.35)^5

you would first go 5 x 1.35 = 6.75.. so now you would add that too 11.. to get 74.25??

But i dont think thats right.. I think im making a mistake somewhere

Answer 6

11(1.35)^5 means 11 times (1.35^5)

so you raise 1.35 to the fifth power first

then you multiply

Answer 7

So you wouldnt multiply 1.35 by 5? you would go 1.35 x 1.35 x 1.35 x 1.35 x 1.35?

Answer 8

So if you did it that way you would get 4.48403344

Answer 9

yes 1.35^5 does not mean 1.35 times 5

it means 1.35 times itself 5 times

Answer 10

Okay so now you have 4.48 x 11 right?

Answer 11

when I use a calculator, I get

11(1.35)^5 = 49.3243678125

make sure you get around the same

Answer 12

I got 49.28

Answer 13

(1.35)^5 = 4.4840334375

then multiply that by 11 to get

11*4.4840334375 = 11*4.4840334375 = 49.3243678125

Answer 14

so you're pretty close

Answer 15

So you have to use the whole number? I was only using 4.48 x 11

Answer 16

well I used up to 15 decimal digits. I just let the calculator store them. Ideally you should use as many decimal digits as possible.

Or you can compute it directly by typing in 11*(1.35)^5

Answer 17

Well when i just type it into a calculator i got 49.3243678

Answer 18

actually, not 15, I guess in this case I'm using 10 decimal digits

Answer 19

looks good

Answer 20

So when it says Numerical Answers Expected.. would i just put 49.32?

Answer 21

Now you'll use the formula

\[\Large m = \frac{f(b)-f(a)}{b-a}\]

Answer 22

Why do i need the formula? I just need to find the distance between year 1 and 5.. wouldnt it be 49.32?

Answer 23

you need to find the difference in y and difference in x

then divide the two

Answer 24

Oh well i have no idea what to do next then.. I thought that was all

Answer 25

\[\Large f(1) = 14.85\]
\[\Large f(5) \approx 49.3243678125\]

so,

\[\Large m = \frac{f(b)-f(a)}{b-a}\]
\[\Large m = \frac{f(5)-f(1)}{5-1}\]
\[\Large m \approx \frac{49.3243678125-14.85}{5-1}\]
\[\Large m \approx \frac{34.4743678125}{4}\]
\[\Large m \approx 8.618591953125\]

Answer 26

The slope of the line through those two points is approximately 8.618591953125

that is equal to the average rate of change (roughly)

Answer 27

So the answer to the question is 8.61?

Answer 28

Because Numerical Answers Expected?

Answer 29

plot the function

Answer 30

plot the points for x = 1 and x = 5