Question

HELP PLEASE!!!!!! MEDALLLLLL!!!
A certain forest covers an area of
3300km2
. Suppose that each year this area decreases by
7.25%
. What will the area be after
14
years? round your answer to the nearest square kilometer.

Answer 1

@Mateaus

Answer 2

@confluxepic

Answer 3

@sammixboo

Answer 4

Do you know how to find how much it has decreased the first year?

Answer 5

No

Answer 6

ok so you have 3300 square kilometers and it says that it decreases 7.25% of the 3300 square kilometer each year. So first you have to find how much is 7.25% of 3300.

Answer 7

Do you know how to find how much is 7.25% of 3300?

Answer 8

no lol

Answer 9

Well to find how much is 7.25% of 3300. First you have to convert the percentage to decimals.

Answer 10

The way you do that is grab 7.25% and divide it by 100. You will get a decimal.

Answer 11

so \[\frac{ 7.25 }{ 100 } = 0.0725\]

Answer 12

once you have this, you can find out how much is 7.25% of 3300. Multiply 3300 to 0.0725 and you will find how much 7.25% is of 3300.

Answer 13

0.0725

Answer 14

239.25?

Answer 15

Yes that is 7.25% of 3300. Now that you have this, we go back to the problem. Since it says that its decreasing 7.25% yearly. That means that 7.25% is decreasing from 3300 or in other words 3300 - 239.25

Answer 16

3060.75

Answer 17

Yes, that is the total amount left after it decreased 7.25% in a year.

Answer 18

you saw that 3300 was squared right?

Answer 19

The question is asking how space will be left after 14 years.

Answer 20

It's kilometer square.

Answer 21

ok so what do i do subtract 3060.75 from 3300?

Answer 22

After a year, it decreased 7.25% so now you have 3060.75km^2

Answer 23

it has to be rounded

Answer 24

to the nearest square km

Answer 25

There is another way to do it but I can't remember. Now what you do is grab 3060.75 and do the same process you did with 3300.

Answer 26

what do you mean?

Answer 27

3060.75 * 0.0725

Answer 28

Since each year is decreasing 7.25%.

Answer 29

then whatever you get out it, subtract it from 3060.75, thats how much km^2 you are left after 2 years.

Answer 30

i got 221.904375

Answer 31

subtract that from 3060.75

Answer 32

2838.845625

Answer 33

Thats how much is left after 2 years.

Answer 34

what do i round it to, 2838.8?

Answer 35

is that rounded to the nearest square km?

Answer 36

You can continue decreasing it until you reach to 14 years or you could use a formula hehe

Answer 37

i dont understand

Answer 38

So first you started with 3300 and after it decreased 7.25% in a year. Now 3300 is 3060.75. Then another year passed and 7.25% decreased from 3060.76 so on the second year there is 2838.8km^2 left of forest.

Answer 39

so how do i get the answer?

Answer 40

Well so far you have done 2 years out of 14 years. And that would take a lot of time, right?

Answer 41

yes

Answer 42

There is a formula you can use: \[A(t) = 3300 ( 1 - 0.0725)^t\] where the 1 is really 100% and 0.0725 = 7.25% but both where divided by 100 so that we can have all in decimal and be usable to solve the problem.

Answer 43

\[A(t) = 3300(.9275)^{14}\] after subtracting 1-0.0725 we end up with .9275 or 92.75% and t(time) = 14 so it's raised to the power of 14

Answer 44

This will basically tell you how much km^2 of forest will be left after 14 years.

Answer 45

so what is it?

Answer 46

Well first solve (.9275)^14

Answer 47

.9275*14?

Answer 48

no 0.9275 to the power of 14

Answer 49

so i have to do that 14 times?

Answer 50

Use a calculator otherwise this would be a long process lol

Answer 51

yeah 0.9275 multiplied by itself 14 times.

Answer 52

Example :\[2^3 = 2*2*2\]

Answer 53

4.881158292?

Answer 54

.3486541637

Answer 55

thats the answer?

Answer 56

A(t) = 3300 ( .3486541637) now multiply both and you will get the answer.

Answer 57

1150.558738

Answer 58

Yep that is the answer

Answer 59

rounded?

Answer 60

to the nearest km

Answer 61

\[1150.56km^2\]

Answer 62

says round to the nearest square km still

Answer 63

so would it be 1151?

Answer 64

Yes, that's right .

Answer 65

The radioactive substance uranium-240 has a half-life of
14
hours. The amount
At
of a sample of uranium-240 remaining (in grams) after
t
hours is given by the following exponential function.

=At430012t14
Find the initial amount in the sample and the amount remaining after
30
hours.
Round your answers to the nearest gram as necessary.