Exponential Growth in Species A and B: Solving for Initial Grams

In summary, Species A doubles every 2 hours and initially there are 6 grams. Species B doubles every 5 hours and initially there are 14 grams. To solve for when they have the same mass, we can use the formula N = N_0 \times 2^{t \over T} and set them equal to each other to solve for t.
  • #1
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Homework Statement


Species A doubles every 2 hours and initially there are 6 grams. Species B doubles every 5 hours and initially there are 14 grams.


Homework Equations





The Attempt at a Solution


I've tried graphing this, but I don't think I have the right equations down. I don't know how to form the equations so I can solve the problem.
 
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  • #2
In general for 'doubling time' problems, we have a simple formula

[tex]N = N_0 \times 2^{t \over T}[/tex]

where N is the number of bacteria after t minutes and T is the time in minutes that it takes to double.

So if that's the relevant equation, attempting a solution should be possible.

EDIT: Although I don't actually know what your question is.
 
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  • #3
jackleyt said:
I don't know how to form the equations so I can solve the problem.

You didn't even say what the problem is.
 
  • #4
*How long until the species have the same mass? Sorry.
 
  • #5
jackleyt said:
*How long until the species have the same mass? Sorry.

Okay so you know the equations by which they grow for each of them, and then you set them equal to each other and solve for t.
 

1. What is exponential growth?

Exponential growth is a type of growth where the rate at which something grows increases over time. In other words, the growth rate is proportional to the current value.

2. How is exponential growth calculated?

The formula for exponential growth is: y = abx, where y is the final value, a is the initial value, b is the growth rate, and x is the number of time periods.

3. How does exponential growth apply to species A and B?

In the context of species A and B, exponential growth refers to the population growth of these two species over time. The initial grams refers to the starting population size of each species, and the growth rate is dependent on factors such as resources, competition, and reproduction.

4. Why is it important to solve for the initial grams in exponential growth?

Solving for the initial grams allows us to understand the starting point of the population and how it has grown over time. This information can be used to make predictions about future population growth and to develop strategies for managing and conserving these species.

5. Can exponential growth continue indefinitely?

No, exponential growth cannot continue indefinitely. Eventually, resources will become limited and the growth rate will slow down. This is known as the carrying capacity, which is the maximum population size that an environment can sustain.

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