Question

Please help I will medal/fan (NO DIRECT ANSWERS) :)
A scientist is studying the growth of a particular species of plant. He writes the following equation to show the height of the plant f(n), in cm, after n days:
f(n) = 8(1.05)^n
Part C: What is the average rate of change of the function f(n) from n = 2 to n = 6, and what does it represent?

Answer 1

Please help @mathway @misty1212 @Australopithecus

Answer 2

I know that aroc=\[\frac{ f(b)-f(a) }{b-a }\]

Answer 3

so you could try \(\frac{f(6)-f(2)}{6-2}\) ?

Answer 4

the average is then 1. I know that the f(b) and f(a) are the y values, and b and a are the x values. @IrishBoy123

Answer 5

\[\frac{ y2-y1 }{ x2-x1 }\]

Answer 6

\(\large \frac{8(1.05)^6 - 8(1.05)^2}{6-2}\)
\(\large = 8\frac{(1.05)^6 - (1.05)^2}{4}\)
\(\large = 2[(1.05)^6 - (1.05)^2]\)

that's shouldn't give you 1

Answer 7

okay then... this is a different equation. Could you help me solve it?

Answer 8

do you see where it came from?

the rest is just pumping it into a calculator

Answer 9

\(f(n) = 8(1.05)^n\)
so
\(f(6) = 8(1.05)^6\)
\(f(2) = 8(1.05)^2\)

Answer 10

okay what exactly would I type into my calculator, it is not hard to get the numbers messed up. Sorry for being such a bish I woke up early.. :( @IrishBoy123

Answer 11

The average rate of change is (change in height)/(change in n)
The change in height is 10.72 - 8.82 = 1.9
The change in n is 6 - 2 = 4
So the average rate of change is 1.9/4 = 0.475
But what is the average rate of change? It is the average daily (because a single change in n corresponds to a day) growth of the plant (because f(n) represents height)

Answer 12

so you got the 0.475. good.

and yes it is the average change per day.

it is a simplification - ie assuming the change per day is the same - becauseit isn't this is an exponential so the change per day increases...

Answer 13

So everything I said was correct? @IrishBoy123 thanks!!

Answer 14

sounded good to me