Suppose you started with 100 bacteria, but they still grew by the same growth factor. Write the function rule for this situation
y=100 x 8^x
y=100 x 4^x
y=8 x 100^x
y=4 x 100^x
It was A. Thank you so much!
y = 100 * n^t
when t = 0 , y = 100 * n^0 = 100*1 = 100
when t = 1, y = 100 n
when t = 2 , y = 100 * n*n etc
Therefore either of the first two work
4 or 8 are growth factor choices. You did not specify if it grows to 4 times in a generation or 8 times
Let's see, if we start with 100 bacteria and they grow by the same growth factor, the correct function rule would be:
y = 100 x 2^x
Because each factor of 2 represents doubling the number of bacteria. But since none of the options given match this rule, I'll have to make a joke instead. Why did the bacteria go to therapy? Because they wanted to multiply their growth potential!
The correct function rule for this situation would be:
y = 100 x 4^x
To determine the correct function rule for a situation where 100 bacteria are growing by the same growth factor, we need to understand the relationship between the initial number of bacteria and the growth factor.
In this case, the growth factor is consistent, meaning each time period has the same rate of growth. We can represent this growth factor with a variable, let's call it "r".
Now, let's break down the given options:
- Option 1: y = 100 * 8^x - This function rule assumes that the growth factor is 8, and the initial number of bacteria is 100. However, it does not account for consistent growth by the same factor.
- Option 2: y = 100 * 4^x - This function rule assumes that the growth factor is 4, and the initial number of bacteria is 100. Again, it does not consider consistent growth.
- Option 3: y = 8 * 100^x - This function rule assumes that the growth factor is the initial number of bacteria (100), but the formula for exponential growth does not match this representation.
- Option 4: y = 4 * 100^x - This function rule assumes that the growth factor is the initial number of bacteria (100), but it does not account for consistent growth.
The correct function rule for this situation would be:
y = 100 * r^x,
where "r" represents the growth factor. Since the question states that the bacteria still grew by the same growth factor, none of the provided options satisfy this condition.