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
Step-by-step explanation:
w(2w - 30) = 5400
2w²- 30w = 5400
2w² - 30w - 5400 = 0
(w - 60 ) ( w + 45 ) = 0
w= 60 w= - 45
only take the positive value
therefore w = 60
Answer:
q.4 's answer is d. miles
q.5 's answer is 3
q.6 's answer is 6
can you tell what the dot means i can tell you the other two's too
