Question

suppose a population of 50 crickets doubles in size every 4 months. how many crickets will there be after 5 years?

Answer 1

Ok so there is 12 months in a year correct?

Answer 2

First of all, Welcome to OpenStudy :D

Answer 3

yes

Answer 4

Ok so then 5x12 is 60 so divide 60 into 4

Answer 5

thats 15

Answer 6

but my answer choices is in the thousands

Answer 7

Shoot my dyslexia got the best of me

Answer 8

Lemme redo that

Answer 9

We should know:
1 year = 12 months

Given: Doubles every 4 months

So:
4 * 3 =12

Therefore:
1 year, there is 3 sets of 4 months. Hence: 4 * 3 = 12

Then:
2 years have 6 sets of 4 months.

3 years have 9 sets of 4 months

4 years have 12 sets of 4 months

5 years have 15 sets of 4 months

Good so far?

Answer 10

\i did all that but i confused myself

Answer 11

We start with a population of 50 crickets

So then:

\[50 \times 2^{n}\]
\[50 \times 2^{15}\]
whats 2^15?
after u get that, multiply what you got from that by 50.
Try it and let me see what you get. :)

Answer 12

50 X 2^15 is 1638400

Answer 13

yes, that's correct. is that one of your answer choices?

Answer 14

^ yes good.

Answer 15

So:
\[1,638,400\]
Is that an answer choice? @roxxy251

Answer 16

You were on the right path @dmezzullo :)

Answer 17

That stuff is easy for me but dyslexia dont help

Answer 18

it was on my quiz, i go it wrong by puttin 1500 buti believe that was 1 of my answer choices,im doing school online, and ihova another question also

Answer 19

Another question from ur quiz?

Answer 20

@roxxy251 just to clarify, are these problems that you got wrong on the quiz?

Answer 21

yes these the problem i had wrong on the quiz

Answer 22

okay. I'm not interested in helping someone take a quiz, but happy to explain after the fact.

Answer 23

yep ^

Answer 24

what was the next one you got wrong? if you can explain what your wrong answer was, and how you got it, that would be great — wouldn't have to worry that you were trying to pull a fast one.

Answer 25

again, yep ^

Answer 26

and we promise not to laugh :-)

Answer 27

suppose an investment of $8,200 doubles in value every 7 years. how much is the investment worth after 28 years

Answer 28

how many doublings is that?

Answer 29

4

Answer 30

right. and what is 2*2*2*2?

Answer 31

16

Answer 32

and 16 * 8200?

Answer 33

yep ^

Answer 34

131200

Answer 35

its kinda the same concept as your 1st question

Answer 36

so how did you get it wrong?

Answer 37

@roxxy251 what did you put as your answer; which was wrong according to you?

Answer 38

86,000 i used the wrong formula and how you putting it make it seemd a whole lot easier, thanks

Answer 39

well, I try :-)

Answer 40

r u very good n math

Answer 41

lol yes @whpalmer4 is quite good; very good, in math :3

Answer 42

Alot of ppl here are!

Answer 43

okay im having problems with exponential growth and decay

Answer 44

okay, let's have one of those problems.

Answer 45

u still there

Answer 46

I am.

Answer 47

this is home work now, and i still dont understand this at all . but the question is, a boat costs 16,600 an decreases in value per 14% per year. how much will the boat be worth after 11 years

Answer 48

Okay. present value is $16,600. Decreases by 14% each year. 14% = 14% * 1/100% = 0.14, right? If we start with 1, and subtract 14%, that's 1-0.14 = 0.86.

After 1 year, the boat is worth 0.86 * purchase price. After 2 years, the boat is worth how much?

Answer 49

14276

Answer 50

ugh i feel dumb

Answer 51

i hate math

Answer 52

No, it's worth that much after 1 year. At the end of 1 year, it has decreased by 14%, which is the same as saying it is worth 86% of its previous value. Each passing year, we'll multiply by 86% again. After n years, the value will be the starting value * 0.86^n — do you see why that is?

Answer 53

no ,n itsmaking me very upset

Answer 54

Okay, do you see why multiplying by 0.86 is the same as decreasing 14%?

Answer 55

nope

Answer 56

what do you think it means to decrease by 14%?

Answer 57

less than

Answer 58

how much?

Answer 59

If I have 100 dollars, and it decreases by 14%, how much do I have left?

Answer 60

im not really good with percentages,

Answer 61

percent just means "out of 100"

14 percent means 14 out of 100.

Answer 62

okay so basically divide 14 over a 100 or subtract 14and 100

Answer 63

if we decrease something by 14%, it means we chop it up into 100 equal pieces, and get rid of 14 of them.

Answer 64

that leaves us with 86 of those pieces

Answer 65

so decreasing by 14% over and over means keeping only 86% over and over...

Answer 66

okay now w/ that problem i suppose to do what

Answer 67

well, you wanted to find out how much the boat is worth after some number of years of depreciation at 14% per year. the value of the boat is going to be the starting value (what ou paid for it) * 0.86 after one year, starting value * 0.86 * 0.86 after two years, starting value * 0.86 * 0.86 * 0.86 after three years, and so on: \(16,600*0.86^n\) where \(n\) is the number of years.

Answer 68

in this case, we want to find how much it is worth after n=11 years. your calculator probably has a y^x button, so you enter 0.86, press y^x, then enter 11, then press * 16600 =