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
Answer:
14.225 kilometers.
Step-by-step explanation:
Monday 3.6
Tuesday 4.705
Wednesday 5.92
By using the addition operation, the total distance, in kilometers, that Andrea ran over the three days will be :
3.6 +4.705 +5.92=14.225
Hence, the total distance that Andrea ran over the three days = 14.225 kilometers.
Answer:
(x + 1)² = (2x)²
(1 + 1)² = (2(1))²
2² = 2²
4 = 4
(-1 + 1)² = (2(-13))²
(-12)² = (-26)²
Not true
x = -13 satisfies neither
Answer:
3
Step-by-step explanation:
-2+1= -1
4-3=1
-3/1= -3
Let the two integers be x and x + 1, then
2(x + 1) + 9 = 3x
2x + 2 + 9 = 3x
3x - 2x = 11
x = 11
Therefore, the integers are 11 and 12.
