Will give medal ......Can someone check my work to see if im doing it right. .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) = 10(1.02)n
When the scientist concluded his study, the height of the plant was approximately 11.04 cm. What is a reasonable domain to plot the growth function?

Question

Will give medal ......Can someone check my work to see if im doing it right. .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) = 10(1.02)n
When the scientist concluded his study, the height of the plant was approximately 11.04 cm. What is a reasonable domain to plot the growth function?

anonymous · Answer

Part a i think the domain to plot  is either (0-5) or (1-5)

anonymous · Answer

@johnweldon1993 @SithsAndGiggles  or anyone else that might be able to check and help me :)

johnweldon1993 · Answer

Well first, think about what the function is

It is the relation of the height of the plant at any given times 'n'

Where the graph crosses the y-axis, is when 'n' = 0...or the beginning height of the plant

johnweldon1993 · Answer

As far as the domain goes, from the equation

$$\large 10(1.02)^n$$

What is the minimum time we can use? well we cant use last week, the data is for now until whenever the plant decides to die

So I would use your (0 to 5) choice

anonymous · Answer

so is my part A and part B is correct @johnweldon1993

johnweldon1993 · Answer

Part A looked good

Part B, specify that it is the height of the plant at time 0 *the starting height*

anonymous · Answer

then part c i would use the formula to find the average rate of change  between n=1 and n=5

johnweldon1993 · Answer

Right

$$\large \frac{f(5) - f(1)}{5 - 1} = ?$$

anonymous · Answer

y^2-y^1 over X^2-X^1

anonymous · Answer

I dont know how you wrote it like that on here lol

anonymous · Answer

Which is 4 over 4 which is= to 1

johnweldon1993 · Answer

Lol learn the latex...use the equation button below the textbox

But wait its 4/4? I know the bottom is 4 but the top doesnt sound right

anonymous · Answer

oh thanks ill try it

anonymous · Answer

would it be f(4)

johnweldon1993 · Answer

No, the way I write f(5) and f(1) simply means what does the function equal when you plug in 5 for n? and what does the function equal when you plug in 1 for n?

anonymous · Answer

so i have to figure out the formula 10(1.02) n which is 10(1.02)5 =which is 11.041

anonymous · Answer

and 10(1.02)1 =10.2

johnweldon1993 · Answer

right!!

anonymous · Answer

$$\frac{ 11.041-10.2 }{ 4}$$

johnweldon1993 · Answer

exactly!

johnweldon1993 · Answer

I'm actually headed out now....but you have it now

anonymous · Answer

which is $$\frac{ 0.841 }{ 4}$$

anonymous · Answer

is that all i need to do :)

anonymous · Answer

Thank you so much for helping me understand this problem @johnweldon1993