# Solving a Word Problem: Algae Increase by Factor of 4 Every 60 Days

• Jimmy84
In summary, the first question asks how many days it will take for the algae to double in size, given that it increases by a factor of 4 every 60 days. The answer is 30 days. The second question asks how many days ago the algae was half its current size, given that it will increase by a factor of 4 every 60 days. The answer is 30 days prior to its current size.
Jimmy84

## Homework Statement

I just translated this word problem:

The zone of a alga increases every 2 month about the factor 4. How many days does the alga needs to increse into the double? How many days ago has the alga been the half?

## The Attempt at a Solution

1.) The first question states

The algae increases by a factor of 4 every 60 days. how many "days" does the alga needs to increse into the double?

So I got 4x = 60 multiplyed 2

x = 30 days

2.) I don't understand the second question.

How many days ago has the alga been the half?

I would appreciate some help, thanks.

The second part wants you to look backwards. The algae is size x at the moment. 30 days from now, you found that the algae would be 2x in size. Using the fact that the algae will increase by a factor of 4 in size over 60 days, how many days ago was the algae 0.5x in size?

singular said:
The second part wants you to look backwards. The algae is size x at the moment. 30 days from now, you found that the algae would be 2x in size. Using the fact that the algae will increase by a factor of 4 in size over 60 days, how many days ago was the algae 0.5x in size?

I tryed 2x = 30 multiplyed by 0.5

= 7.5 days ago is that right?

thanks

Jimmy84 said:
I tryed 2x = 30 multiplyed by 0.5

= 7.5 days ago is that right?

thanks

If the algae increases by a factor of 4 every 60 days, then 60 days prior to the algae being size x (at present), the algae will be 0.25x. Starting from 0.25x, how long will it take for the algae to increase to 0.5x?

## 1. How do you determine the rate of increase for algae?

The rate of increase for algae can be determined by dividing the factor of increase (4) by the number of days (60). In this case, the rate of increase would be 4/60 = 0.067, meaning the algae population increases by 0.067 every day.

## 2. How many days will it take for the algae to double in population?

To determine the number of days it takes for the algae to double in population, we can use the formula t = log2/log(1+r), where t is the number of time periods (days) and r is the rate of increase. Plugging in the values, we get t = log2/log(1+0.067) = 10.36 days. Therefore, it takes approximately 10 days for the algae population to double.

## 3. Can this equation be used to predict the algae population in the future?

Yes, this equation can be used to predict the algae population in the future as long as the rate of increase remains constant. However, external factors such as competition, predation, and environmental changes can affect the actual population growth.

## 4. How can we solve word problems involving exponential growth?

To solve word problems involving exponential growth, we first need to identify the initial value, the rate of increase, and the time period. Then, we can use the formula A = A0 * (1+r)^t, where A is the final value, A0 is the initial value, r is the rate of increase, and t is the time period. Plug in the values and solve for the unknown variable.

## 5. Is there a limit to how much the algae population can increase?

Yes, there is a limit to how much the algae population can increase. This is known as the carrying capacity, which is the maximum number of organisms that an environment can support. Once the carrying capacity is reached, the population growth will slow down and eventually reach a stable level.

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