Question

Assuming these rates remain constant, what can you do to get a better approximation of when the two beaches will have the same width?

Answer 1

Question #3

Answer 2

Assuming you already did part (B) you know that they have the same width somewhere between years 11 and 12. To get a better approximation there are a few things you could do:

1) Find data readings on a finer scale than 1-year (every 6-months, every month etc.)
2) Run a linear interpretation between the two years for each beach using a guess-and-test method to find a common reading.
3) Plot both sets of data a see where the liens cross.
4) Derive a function for both sets of data and find the point of intersection.

Answer 3

Can you help me another problem?

Answer 4

Sure.

Answer 5

#4

Answer 6

To start lets call the number of pine trees 'p' and the number of oak trees 'k' (not using a letter 'oh' becasue it looks too much like a 0/'zero').

We know that right now:
\[p=800\] and \[k=50\]

Answer 7

The equation for pine trees is 800-0.05x and oak trees 50-0.15x=fx

Answer 8

Not quite no. Lets think about it. After one year there will be 5% less pine tress or to say it another way there will be 95% left. We can write this one of two ways:

\[p2=0.95p1\] or \[p2=p1-0.05p1\] Similarly for the oak tress we have:

\[k2=1.15k1\] or \[k2=k1+0.15k1\]

Answer 9

For future years we lose another 5%, buts it NOT 5% of the original, it's 5% of what was left over.

Answer 10

So:

\[p3=0.95p2=0.95(0.95p1)\] or to write it another way:
\[p3=p1(0.95)^{2}\] The thing to notice here is this: we have now gone 2 years and our exponent is 2.

What would the equation be after 3 years?

Answer 11

Third power but I don't get it

Answer 12

Where'd u get 95 from

Answer 13

0.95 is from 95%, If we loose 5% we have 95% left.

Answer 14

So our full equations would be; \[p=800*(0.95^{X})\] and \[k=50*(1.15^{X})\] where 'x" is the number of years.

Answer 15

If we plot both of those we get this (Attachment)

Answer 16

And by looking at the graph we can see that we have the same number of oak and pine somewhere between years 14 and 15.

Answer 17

What years do 14 and 15 represent? 2015?

Answer 18

If we want the answer exactly we can solve for 'X': and we get x = 14.512 so a little more than 14 years 6 months.

Answer 19

They don't don't tell us when year zero is so we can't know. If we say that year zero is right now then year 14 is 2024.

Answer 20

There will be 400 trees during that time?

Answer 21

I didn't work it out but there would be about 390 at year 14 and about 380 or so at year 15.

Answer 22

It's for letter C

Answer 23

Ya 390 at year 14:

\[800*(0.95^{14})=390.1\] but you can't have 0.1 of a tree.....

Answer 24

If you were just reading it off the graph 400 would be a good approximation.

Answer 25

Okay so I can say approximately 400

Answer 26

Yes.