Exponential Word Problem - I'm very confused

[pmahoney1337]

I would love to show some effort here, but I honestly have no idea were to start, any help would be greatly appreciated.

Initially there are two snow goons. We need to estimate the amount of time it takes each snow goon to make 100 new snow goons. Let t = the number of days since the first two snow goons were made. Let N(t) = the number of snow goons on day t.
Estimate: On day t = 3 we estimate that there will be 100 snows goons.


1. On day t = 0 there are N = ____ snow goons. This is the initial amount.
The blank is 2 I'm assuming.

2. Find a function of the form N(t) = (C)e^kt that gives N(t), the number of snow goons that exist t days after the first two are built.

 

[wjm11]

[h=2]Exponential Word Problem - I'm very confused[/h] [FONT=&quot]I would love to show some effort here, but I honestly have no idea were to start, any help would be greatly appreciated.

Initially there are two snow goons. We need to estimate the amount of time it takes each snow goon to make 100 new snow goons. Let t = the number of days since the first two snow goons were made. Let N(t) = the number of snow goons on day t.
Estimate: On day t = 3 we estimate that there will be 100 snows goons.


1. On day t = 0 there are N = ____ snow goons. This is the initial amount.
The blank is 2 I'm assuming.

2. Find a function of the form N(t) = (C)e^kt that gives N(t), the number of snow goons that exist t days after the first two are built. [/FONT]

Your job is to determine the values of C and k. You have two data points: (0,2) and (3,100). Plug them into your equation to determine C and k.

N(0) = Ce^(k(0)) => 2 = Ce^0 = C(1) => C = 2

N(3) = 2e^(k(3)) => 100 = 2e^(3k)
50 = e^3k
ln(50) = ln(e^3k) = 3k
k = ln(50)/3

Make sense?

 

[pmahoney1337]

Yes, I got that far myself actually, but now it is asking me to find the number of snow goons after 1 week.

So would I just plug the answer for the last problem in for k and 7 for t into the equation: N(t) = 2e^kt then solve for N(t)?

 

[wjm11]

I got that far myself actually

(Then why didn't you say so?)

So would I just plug the answer for the last problem in for k and 7 for t into the equation: N(t) = 2e^kt then solve for N(t)?

Yes.

 

[pmahoney1337]

(Then why didn't you say so?)



Yes.

I didn't say so because I made this thread before I figured that part out. Eventually I figured it out and then thought I might as well confirm what I do next.
Thanks for your help.

 

[pmahoney1337]

I didn't say so because I made this thread before I figured that part out. Eventually I figured it out and then thought I might as well confirm what I do next.
Thanks for your help.

Ok, I'm stuck again on this. Sorry for having to bump this up.

So after doing calculations I figured out that there will 51.5764 snow goons after 1 week and 2689.3429 after 1 year.

This is the equation I used. N(t) = 2e^(ln(50)/3)(7) and (365)

The next question asks after how many days will there be 1 million snow goons. So I plug 1 million in for N and solve for t. I end up getting 10. That doesn't make sense according to my previous answers for 1 week and year. Any help as to what I could be doing wrong?

This is the equation I used. 1,000,000 = 2e^(ln(50)/3)t

EDITED with information browser crashed in the middle of post.

 

[mmm4444bot]

N(t) = (C)e^kt

You need to insert grouping symbols around exponents.

N(t) = C*e^(kt)

 

[mmm4444bot]

So after doing calculations I figured out that there will 51.5764 snow goons after 1 week and 2689.3429 after 1 year.

This is the equation I used. N(t) = 2e^(ln(50)/3)(7)

The red parentheses show the exponent, so the factor 7 needs to be inside them.

This is the equation I used. 1,000,000 = 2e^(ln(50)/3)t

The factor t should appear inside the red parentheses.

Your values above for N(7) and N(365) are not correct, but t = 10 days looks correct for a million snow goons.

We need to place grouping symbols around the entire exponent, especially if we're entering these expressions into a calculator.

The Commutative Property of Multiplication says that we may change the order of factors, so we may write:

N(t) = 2*e^(7*ln(50)/3)

1000000 = 2*e^(t*ln(50)/3)

Perhaps, this texting is more clear?

Try your calculations again for t = 7 and t = 365.

 

[pmahoney1337]

Your values above for N(7) and N(365) are not correct, but t = 10 days looks correct for a million snow goons.

We need to place grouping symbols around the entire exponent, especially if we're entering these expressions into a calculator.

The Commutative Property of Multiplication says that we may change the order of factors, so we may write:

N(t) = 2*e^(7*ln(50)/3)

1000000 = 2*e^(t*ln(50)/3)

Perhaps, this texting is more clear?

Try your calculations again for t = 7 and t = 365.

Thanks, turns out I was indeed just misinforming my calculator. It makes sense now

 

[mmm4444bot]

Glad you figured it out.

BTW, I found the following wording a bit confusing, in this exercise. Why do they use the word "each"?

there are two snow goons. We need to estimate the amount of time it takes each snow goon to make 100 new snow goons

 

[pmahoney1337]

I have know idea. It confused the **** out of me and it literally has no relevance to any of the questions.

 

[pmahoney1337]

For your benefit: I have NO idea

Wow, I have NO idea why I used "know" there, that is something I never do and is a horrendous error that is causing chaos throughout the site. Just so you know... It was just a mistake, I didn't actually believe at the time that was correct. My grammar is actually pretty **** good compared to most people on the interwebs.