Answer:
Step-by-step explanation:
Let the rate at which the bacteria grow be represented by the exponential equation
P(t) = P0e^kt
P(t) is the population of the bacteria after time t
P0 is the initial population
k is the constant of variation
t is the time
If the initial Population is 160 bacteria's, them the equation becomes;
P(t) = 160e^kt
b) if After 5 hours there will be 800 bacteria, this means
at t = 5 p(t) = 800
Substitute and get k
800 = 160e^5k
800/160 = e^5k
5 = e^5k
Apply ln to both sides
Ln5 = lne^5k
ln5 = 5k
k = ln5/5
k = 0.3219
Next is to calculate the population after 7hrs i.e at t = 7
P(7) = 160e^0.3219(7)
P(7) = 160e^2.2532
P(7) = 160(9.5181)
P(7) = 1522.9
Hence the population after 7houra will be approximately 1523populations
c) To calculate the time it will take the population to reach 2790
When p(t) = 2790, t = ?
2790 = 160e^0.3219t
2790/160 = e^0.3219t
17.4375 = e^0.3219t
ln17.4375 = lne^0.3219t
2.8587 = 0.3219t
t = 2.8587/0.3219
t = 8.88 hrs
Hence it will take approximately 9hrs for the population to reach 2790
Always because the higher the negative he less its and the same for he positive side
equation would be 23 plus 9 equals 32 or p, the number of cans she bought
<span>The answer to this question would be: A. the number of adults
</span>
In this question, there are 4 times as many students as adults going on the trip. If we put it into a function where s= student and a=adult, then we could get one equation:<span>
1. s=4a
</span><span>
Each student ticket cost $2 and each adult ticket cost $4. The total cost of the trip is $144. We also can get one equation for this
2. 2s+ 4a= 144
If you put the first equation into the second, you will get:
</span>2s+4a= 144
2(4a)+4a= 144
The function is already similar with <span>2(4x)+4x but it uses a instead of x. Then x = a = number of adult</span>
