Answer:
327
Step-by-step explanation:
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)
Answer:
n=8
Step-by-step explanation:
Answer:
Step-by-step explanation: <u>Speed</u> is distance an object travelled per unit time.
It is represented by letter v and can assume various units.
1) ![v=\frac{distance}{time}=\frac{d}{t}](https://tex.z-dn.net/?f=v%3D%5Cfrac%7Bdistance%7D%7Btime%7D%3D%5Cfrac%7Bd%7D%7Bt%7D)
![v=\frac{90}{5}](https://tex.z-dn.net/?f=v%3D%5Cfrac%7B90%7D%7B5%7D)
v = 18 miles per hour
Her average speed is 18 mph.
2) Rearraging formula for distance:
d = v.t
d = 70 * 4
d = 280 miles
You would travel 280 miles.
3) ![v=\frac{d}{t}](https://tex.z-dn.net/?f=v%3D%5Cfrac%7Bd%7D%7Bt%7D)
![v=\frac{315}{6}](https://tex.z-dn.net/?f=v%3D%5Cfrac%7B315%7D%7B6%7D)
v = 52.5 mph
My average speed is 52.5 mph.
4) Rearranging formula to determine time:
![t=\frac{d}{v}](https://tex.z-dn.net/?f=t%3D%5Cfrac%7Bd%7D%7Bv%7D)
![t=\frac{210}{90}](https://tex.z-dn.net/?f=t%3D%5Cfrac%7B210%7D%7B90%7D)
t = 2.34 hours
It will take 2 hours and half to arrive in Leeds. So, we will be expected to arrive at 12:04.
5) The unit change but the way of calculating time is the same.
![t=\frac{2000}{4}](https://tex.z-dn.net/?f=t%3D%5Cfrac%7B2000%7D%7B4%7D)
t = 500 s
or t = 8.34 minutes
It will take, for an athlete to run 2000m, 8.34 minutes.
6) a) All units must match, so for a speed in mph:
45 minutes is 0.75 hours. Total time is 8.75 hours.
![v=\frac{420}{8.75}](https://tex.z-dn.net/?f=v%3D%5Cfrac%7B420%7D%7B8.75%7D)
v = 560 mph
The average speed is 560 mph.
b) ![t=\frac{d}{v}](https://tex.z-dn.net/?f=t%3D%5Cfrac%7Bd%7D%7Bv%7D)
![t=\frac{420}{63}](https://tex.z-dn.net/?f=t%3D%5Cfrac%7B420%7D%7B63%7D)
t = 6.67 hours
Sam will take 6.67 hours to covered the distance.