Question

Tony has been planting strawberries in a garden in his backyard. Tony started with strawberries in one square foot of garden modeled by the function s(x) = 20. He is allowed to convert more of the garden, and each additional square foot he maintains allows his strawberry plants to produce more by a rate of a(x) = 1.2^(x-1).

Explain to Tony how to create an equation to predict the number of strawberries he can expect based on the number of square feet he maintains. Describe how to determine the number of strawberries he will grow with 15 square feet.

Answer 1

This doesnt seem to make sense to me..
for s(x) = 20
shouldnt this be
s(x)=20x?
what if x is 30, is it still just 20?

Answer 2

do we multiply the two functions or just add them? how do they combine?

Answer 3

I created
f(x) = 20 + 1.2^(x-1)
but this doesnt seem right,

Answer 4

it seems more like the strawberries per square foot.
wouldnt you want to multiply this by x somehow?
I mean if 1 sq ft makes 20 strawberries, why would 2 sq ft only make 21?

Answer 5

Ouchh, Its confusing, have A look at it...

Ref: http://openstudy.com/study#/updates/535965dbe4b0f8d836a7ad58

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Answer 6

that other post made no sense to me.

okay so the solution is to multiply these two functions together, not add.

if you were producing 20 strawberries in a square foot, then if you double the square footage you should produce 40 strawberries.. but it also increases the productivity of the plants by 20%.

Therefore
f(x) = 20(1.2^(x-1))

Answer 7

i soooo totally get what your saying it DOES NOT MAKE SENSE

Answer 8

Hi Jasmine, yeah there are a lot of really poorly worded problems in that module. I aced that module with 100% but I had to argue with the teacher to get that because the module is broken, so be on alert and be ready to argue your case, because at least one question will always return a fail no matter what you answer, unless they fixed it, which I doubt because your teacher has no control over the module, they can only grade you. This question though is not broken, it's just worded to trick you.

And dont trust Koikkara's link, all those people in that post are flat out WRONG! and confused. Even though pwnbunny has 11+s on his answer at this time.. it's wrong. Let me explain and perhaps you'll trust me on this one.

In the first equation we know that Tony's garden currently only has 1 square foot of area, we can assume in a single plant, so given the function s(x)=20, then x="the square footage of the area", and we can assume that x=1. Therefore our strawberry function of s(x)=20 is currently s(1)=20 strawberries produced.

The problem then states that as the square footage of the garden increases, it's productivity increases at a rate of 20% per extra sq foot, hence the 1.2 because (1 + (20% of 1))=1.2

Here is where the question is designed to trick you, because your natural assumptions are that if you double the square footage of the GARDEN you should have 2 times the strawberries. But you need to think of this as a single PLANT that increases in size and as it increases 1 square foot in size, it's total production only increases by just 20%.

This condition of productivity increase can be described by a function lets say ..
g(x)=1.2 and raise it to the power of (x-1) so each +1 of square footage increases
by 1 foot. and you get. this function. It's one of those standard growth functions you've been learning about similar to growth given an interest rate over a term.
g(x)=1.2^(x-1)

If you examine what that function puts out for different values of x you get..
g(1) = 1.2^(1-1)=1.2^0=1
g(2) = 1.2^(2-1)=1.2^1=1.2
g(3) = 1.2^(3-1)=1.2^2= 1.44
and so on it goes..

Now if you take that original function s(x) and multiply it by g(x) what do you get?

Given:
s(x)=20
g(x)=1.2^(x-1)
Equation:
f(x) = s(x) * g(x)
Then:
f(x) = 20(1.2^(x-1))

Can you see why you want to multiply these functions and not just add them?
and also do you see why you don't just want to multiply 1.2 by (x-1)? As pwnbunny did?

If we test the values of this function to see what you get..
f(1) = 20 * 1.2^(1-1)=1.2^0= 20 * 1 = 20
f(2) = 20 * 1.2^(2-1)=1.2^1= 20 * 1.2 = 24
f(3) = 20 * 1.2^(3-1)=1.2^2= 20 * 1.44 = 28.8

This describes more accurately a single PLANT that when it increases its footage by 1 square foot, it increases productivity by 20%.

If you work out what pwnbunny's function will give you.. instead of exponentially growing the plant production by 20% you at first kill all production and then grow at a linear rate of 1.2 strawberries per extra foot. You know this has to be wrong.
Given
p(x) = 20 + (1.2(x-1))
p(1) = 20 * 1.2(1-1)=20 + 1.2(0)= 20 + 0 = 20
p(2) = 20 * 1.2(2-1)=20 + 1.2(1)= 20 + 1.2 = 21.2
p(3) = 20 * 1.2(3-1)=20 + 1.2(2)= 20 + 2.4 = 22.4
p(4) = 20 * 1.2(4-1)=20 + 1.2(3)= 20 + 3.6 = 23.6

Try plotting the functions on a chart and you'll see what I mean.