Answer:
(13)
<u>x= 8</u>
<u>y=11</u>
(14)
<u>x= 20</u>
<u>y=20.75</u>
(15)
<u>x=9</u>
<u>y=13</u>
Step-by-step explanation:
(13) 8x-1 = 11x -25
24=3x
<u>x= 8</u>
8(8)-1 +15y-48= 180
15y=165
<u>y=11</u>
(14) 7x-44 + 4x + 4= 180
11x= 220
<u>x= 20</u>
4(20)+4+39= 8y-43
123=8y-43
166=8y
<u>y=20.75</u>
(15) 12x+1=15x-26
3x=27
<u>x=9</u>
28+15(9)-26+4y-9=180
4y=52
<u>y=13</u>
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:
37.68
Step-by-step explanation:
12 times 3.14 = 37.68
Answer:
1.5 hours
Step-by-step explanation:
