# Exponential Word Problem

• Nov 27th 2011, 04:11 PM
pmahoney1337
Exponential Word Problem
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.

Wouldn't the number of snow goons just double everytime? I think the wording is throwing me off or I am over thinking this. Thanks.
• Nov 27th 2011, 04:27 PM
skeeter
Re: Exponential Word Problem
Quote:

Originally Posted by 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.

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.

Wouldn't the number of snow goons just double everytime? I think the wording is throwing me off or I am over thinking this. Thanks.

$\displaystyle N(0) = 2$

$\displaystyle N(t) = 2e^{kt}$

want to solve for t when $\displaystyle N(t) = 102$

$\displaystyle 102 = 2e^{kt}$

you need another bit of info about the population after t = 0 to determine the growth constant k , then you'll be able to find t
• Nov 27th 2011, 04:42 PM
pmahoney1337
Re: Exponential Word Problem
Hmmm, that's weird because I gave you all the information I'm given.

There is a part before that question that asks me to make an estimate of how many snow goons there would be after t amount of days, but I don't see how an estimate would help here.
• Nov 27th 2011, 05:48 PM
pmahoney1337
Re: Exponential Word Problem
I edited the original problem so maybe it is solvable now.
• Nov 27th 2011, 06:04 PM
skeeter
Re: Exponential Word Problem
Quote:

need to estimate the amount of time it takes each snow goon to make 100 new snow goons.
edit the equation ...

$\displaystyle 202 = 2e^{kt}$

Quote:

Estimate: On day t = 3 we estimate that there will be 100 snows goons.
$\displaystyle 100 \approx 2e^{k \cdot 3}$

solve an estimate for k, then use the result to estimate t in the first equation.
• Nov 27th 2011, 06:10 PM
pmahoney1337
Re: Exponential Word Problem
EDIT: Never mind I get it. Thanks, I'll keep posting if I have questions.
• Nov 27th 2011, 06:27 PM
pmahoney1337
Re: Exponential Word Problem
Ok I did what you said and got 202 = (2)e^1.3(3.55). Not sure if that is right, but even if it is I need the function to give me N(t) right?

So would the answer be N(t) = (2)e^(1.3)t?