A colony of bacteria is growing by 23% every other week. What is the equation that models this situation. Let A(t) be the number of bacteria after t weeks and b be the original number of bacteria.
A(t) = b * (1 + .23)^(t / 2)
The equation that models this situation is:
A(t) = b * (1 + 0.23)^t
Where:
- A(t) is the number of bacteria after t weeks.
- b is the original number of bacteria.
- 0.23 represents the growth rate of 23% (converted to decimal form as 0.23).
- t represents the number of weeks.
To model the situation, we need to consider that the colony of bacteria is growing by 23% every other week. Let's break down the problem step by step.
1. Let's first find the growth factor. The growth factor is calculated by adding 1 to the percentage growth rate, expressed as a decimal. In this case, the growth factor is 1 + (23% / 100) = 1.23.
2. Now, let's denote the original number of bacteria as 'b' and the number of weeks as 't'. The number of bacteria after t weeks can be represented as A(t).
3. The growth of the bacteria is compounded each week. Since the colony is growing every other week, we need to account for the multiplication occurring every other week. This can be done by squaring the growth factor for every two weeks. Thus, the equation becomes: A(t) = b * (1.23)^((t/2)).
In summary, the equation that models this situation is A(t) = b * (1.23)^((t/2)).