Question

Help needed... Will fan and medal

Answer 1

Sally has been planting squash in her garden. Sally started with squash in one square foot of garden modeled by the function s(x) = 8. She is allowed to convert more of the garden, and each additional square foot she maintains allows her squash plants to produce more by a rate of\[a(x)=2.4^{x-2}\]Explain to Sally how to create an equation to predict the number of squash she can expect based on the number of square feet she maintains. Describe how to determine the number of squash she will grow with 10 square feet. Use complete sentences.

Answer 2

Anyone?

Answer 3

I think the 8 = the number of squash in 1 square foot
so s(1)=8

Answer 4

It's geometric series

Answer 5

You're still here ?

Answer 6

Yes

Answer 7

Can you help?

Answer 8

She can combine the both equations by multiplying them together to get a function that predicts the number of squash she can expect based on the number of square feet she maintains.

Here, \(s(x) = 8\) represents the starting squash, its the first term in geometric sequence.
Since each additional square foot she maintains allows her squash plants to produce more by a rate of \(a(x)=2.4^{x-1} \), the function for predicting the number of squash is :

\(\large t(x) = s(x) * a(x) = 8*2.4^{x-1}\)

Answer 9

To get the number of squash in 10 square feet of land, simply plugin x = 10 in above equation and evaluate :

\(\large t(10) = 8*2.4^{10-1} = ?\)

Answer 10

except it would be 10-2, right?

Answer 11

@rational

Answer 12

And do I not need to do anything with the 8 as the number of square feet goes up?
s(x)=8 (for 1 square foot)
so would s(x)=16 for 2 square feet?
@rational

Answer 13

@phi what do you think on this?

Answer 14

@SithsAndGiggles

Answer 15

Yes, just calculate it for 10-2 and you're done.

Answer 16

s(x) = 8 is just the first term for 1 square foot.
the growth is modeled by a(x).