Answer:
The initial population was 2810
The bacterial population after 5 hours will be 92335548
Step-by-step explanation:
The bacterial population growth formula is:
![P = P_0 \times e^{rt}](https://tex.z-dn.net/?f=P%20%3D%20P_0%20%5Ctimes%20e%5E%7Brt%7D%20)
where P is the population after time t,
is the starting population, i.e. when t = 0, r is the rate of growth in % and t is time in hours
Data: The doubling period of a bacterial population is 20 minutes (1/3 hour). Replacing this information in the formula we get:
![2 P_0 = P_0 \times e^{r 1/3}](https://tex.z-dn.net/?f=2%20P_0%20%3D%20P_0%20%5Ctimes%20e%5E%7Br%201%2F3%7D%20)
![2 = e^{r \; 1/3}](https://tex.z-dn.net/?f=2%20%3D%20e%5E%7Br%20%5C%3B%201%2F3%7D%20)
![ln 2 = r \; 1/3](https://tex.z-dn.net/?f=ln%202%20%3D%20r%20%5C%3B%201%2F3%20)
![ln 2 \times 3 = r](https://tex.z-dn.net/?f=ln%202%20%5Ctimes%203%20%3D%20r%20)
![2.08 \% = r](https://tex.z-dn.net/?f=2.08%20%5C%25%20%3D%20r%20)
Data: At time t = 100 minutes (5/3 hours), the bacterial population was 90000. Replacing this information in the formula we get:
![90000 = P_0 \times e^{2.08 \; 5/3}](https://tex.z-dn.net/?f=90000%20%3D%20P_0%20%5Ctimes%20e%5E%7B2.08%20%5C%3B%205%2F3%7D%20)
![\frac{9000}{e^{2.08 \; 5/3}} = P_0](https://tex.z-dn.net/?f=%5Cfrac%7B9000%7D%7Be%5E%7B2.08%20%5C%3B%205%2F3%7D%7D%20%3D%20P_0%20)
![2810 = P_0](https://tex.z-dn.net/?f=2810%20%3D%20P_0%20)
Data: the initial population got above and t = 5 hours. Replacing this information in the formula we get:
![P = 2810 \times e^{2.08 \; 5}](https://tex.z-dn.net/?f=P%20%3D%202810%20%5Ctimes%20e%5E%7B2.08%20%5C%3B%205%7D%20)
![P = 92335548](https://tex.z-dn.net/?f=P%20%3D%2092335548)
Length X width = area. for this problem, just divide the area of 756 sq. inches by the length of 108 in. to find the width.
In the case of exponential functions, the graph is shifted when a constant is added to the exponent of the constant. The original equation, f(x) is:
f(x) = (1/2)ˣ
Now, when horizontal shifting is occurring, the equation is:
y = Cˣ⁺ᵃ
If a is positive, the graph shifts to the lefts and the shift is equal to a units. If a is negative, the graph shifts to the right and the shift is equal to a units. Therefore, to shift the graph 3 units to the left:
g(x) = (1/2)⁽ˣ⁺³⁾
The correct answer is B.
Answer:
is there a pic?
Step-by-step explanation: