How Do I Find the Time for Halibut Biomass to Reach 10% of Carrying Capacity?

[Bionerd]

Homework Statement

This problem is driving me crazy because it seems so simple yet I can't get the right answer. We're looking for how long it takes for the biomass of halibut to get within 10% of carrying capacity (look below).

Homework Equations

We have to use this formula: y(t)= 8x10^7/(1+3e^-.71t)

The Attempt at a Solution

I don't even know. How do I find t without knowing y(t)? Everyone I've asked so far has said, "Just plug in". Just plug in what? I know M needs to be changed, and that's about it. The correct answer is 4.6. I'm so confused. Help please?

 

[Hurkyl]

What are y and t?
What is "carrying capacity"?
What is M?

 

[Bionerd]

M is carrying capacity (10% of 8x10^7), t is time (which I'm looking for), and y(t) is the population. I'm confused because I don't have t or y(t).

 

[Hurkyl]

Well, how does biomass relate to anything? Proportional to population, I suppose? You should name the constant of proportionality, if it's going to be relevant.

The carrying capacity is 10% of 8 * 10^7? That seems an odd definition; why the 10%? Anyways, I suppose from context that it's a measure of biomass.

Well, you know what 10% of the carrying capacity is. (right?) That seems like a place to start.

 

[Bionerd]

Biomass is just the math book's way of saying population.

So I'm looking for the time at which population, y(t), is within 10% of carrying capacity (M, which equals 8.7x10^7). My problem is that I don't know y(t), so how do I find t? Should I plug in, say, t=0 and find y(0), then use that to find the other t? That doesn't make sense to me, since population is changing, but it's the only way I can phathom.

 

[Hurkyl]

Well, you do know a the value of

y(the time when the biomass is within 10% of the carrying capacity),

right?



I guess since you're trying to answer "how long", you need a starting time and an ending time. The ending time would presumably be

the time when the biomass is within 10% of the carrying capacity,

does the problem give an indication of the starting time? With no other information, I'd probably guess that you start waiting when time = 0.