+0

# Functions and Modeling

0
89
29
+115

A certain population declines by 4% each year. What is the percentage decline each month? (Round your answer to two decimal places.)

An investment declines in value by 5% each month. By what percentage does its value decline in a year? (Round your answer to two decimal places.)

Mar 25, 2020

#1
+1956
+1

1) Since there are 12 months in a year...

-4/12 will be -1/3% or -0.33 decrease each month

Mar 25, 2020
#3
+115
0

it was .34

Shaezy  Mar 25, 2020
#24
0

A - 1.04^(1/12) =1.00327373 - 1 x 100 =0.33 % - percntage decline per month.

B -1.05^12 =1.795856 - 1 x 100 =79.59% - percentage decline in 1 year.

Guest Mar 25, 2020
#26
+115
0

They are both incorrect, the first one was .34 and the second one is incorrect. I have one more attempt.

Shaezy  Mar 25, 2020
#2
+1956
+1

2) There are 12 months in a year....

-5*12=-60.

It declines by 60% or 0.6 each year.

Mar 25, 2020
#5
+115
0

the 2nd part is also incorrect. These questions are over constant percentage change, so they use formulas like a=1+r for growth and a=1-r for decay. Im stressing out badly because they are super confusing.

Shaezy  Mar 25, 2020
#4
+1956
+1

0.34?! What?!!!!

Mar 25, 2020
#7
+115
0

you were close though. and I appreciate you taking the time to try and help me.

Shaezy  Mar 25, 2020
#6
+1956
+1

I'm confused too... I'm so sorry about my incorrect answers. I will look at them again right now!

Mar 25, 2020
#8
+115
0

no worries lol, I have a few more attempts on the others before they are completely wrong.

Shaezy  Mar 25, 2020
#9
+1956
+1

Okay. Don't trust me 100%, though. I'm a really rushed, angry elementary school kid... LOL!

Mar 25, 2020
#11
+115
0

An elementary school kid?? No way.

Shaezy  Mar 25, 2020
#10
+1956
+1

Is it (0.2)^12

Mar 25, 2020
#13
+115
0

that isn't it either lol.

Shaezy  Mar 25, 2020
#12
+1956
+1

Yes elementary school.... Really!!!!!!!!!! Anyway, is it correct?

Mar 25, 2020
#15
+115
0

that's amazing!!! When I was in elementary I didn't learn this. It was the basics of math. So kuddos!

Shaezy  Mar 25, 2020
#29
+41
0

I see I'm not the only one who is in elementary school here, I'm in fifth grade.

Zekken  Apr 3, 2020
#14
+1956
+1

CPhill? Melody? GET IN HERE!!!!!
LOL

Mar 25, 2020
#16
+115
0

hahahaha

Shaezy  Mar 25, 2020
#17
+1956
+1

LOL!

I got the answer for the other one you asked, though. It's 0.03

Mar 25, 2020
#18
+115
0

Shaezy  Mar 25, 2020
#19
+1956
+1

Yep! Is it right?

CalTheGreat  Mar 25, 2020
#21
+115
0

I haven't tried because I don't think it is correct and this is my last attempt.

Shaezy  Mar 25, 2020
#20
+1956
+1

Oh, wait! Geno's here!!!!!!!

Mar 25, 2020
#22
+20883
+1

One of the compound interest formula is:  F  =  A(1 + x )t

where  F  =  final amount

A  =  initial amount

x  =  interest rate, as a decimal

t  =  number of years

For this problem, if the inital population = A, then the final population will be 0.96A (because it decreased by 4%).

So:                                                    0.96A  =  A(1 + x)12

Divide both sides by A:                       0.96  =  (1 + x)12

Find the 12th root of 0.96:    0.9966039468  =  1 + x

Subtract 1:                                                x  =  -0.003396                  (the '-' indicates that it is decreasing)

Mar 25, 2020
#28
+115
0

That would be correct because the answer was .34. Where were you sooner?! lol Im kidding, thank you though!!

Shaezy  Mar 25, 2020
#23
+1956
+1

You haven't? Okay... makes sense. Try messaging CPhill or Melody.

Mar 25, 2020
#25
+111321
+1

An investment declines in value by 5% each month. By what percentage does its value decline in a year? (Round your answer to two decimal places.)

Let A  be   the value of the investment at the beginning  of the year

At the  end of the year, the investment will be worth

A(.95)^12  ≈  .54036 A

So......the %  decline in one year =  1 -.54036  ≈   45.964% ≈  45.96%

Mar 25, 2020
#27
+115
0

Awesome, thank you! That is how we did it in class but I get confused when it asks for years and months.

Shaezy  Mar 25, 2020