A scientist is studying three different cultures of bacteria {labeled "A", "B" and "C"} and wants to mathematically model the bacterial change of each type. To do this, the scientist decides to collect data for 25 consecutive days and builds the following scatter diagrams where the horizontal axis corresponds to "t" and the vertical axis to the amount of bacteria present in the culture P = P (t) Help the scientist decide which mathematical model (initial value problem) to use for each of the three types of crops. To do this, associate each of the graphs above with one of the following initial value problems. Crop type A a) dP/dt = k with P(0)=P0 and k>0. b) dP/dt = k with P(0)=P0 and k<0. c) dP/dt = kt with P(0)=P0 and k>0. d) dP/dt = kt with P(0)=P0 and k<0. e) dP/dt = kP with P(0)=P0 and k>0. f) dP/dt = kP with P(0)=P0 and k<0. g) dP/dt = kP(1-P/M) with P(0)=P0 and M, k>0. h) dP/dt = kP(1-P/M) with P(0)=P0 and M, k<0. Crop type B a) dP/dt = k with P(0)=P0 and k>0. b) dP/dt = k with P(0)=P0 and k<0. c) dP/dt = kt with P(0)=P0 and k>0. d) dP/dt = kt with P(0)=P0 and k<0. e) dP/dt = kP with P(0)=P0 and k>0. f) dP/dt = kP with P(0)=P0 and k<0. g) dP/dt = kP(1-P/M) with P(0)=P0 and M, k>0. Crop type C a) dP/dt = k with P(0)=P0 and k>0. b) dP/dt = k with P(0)=P0 and k<0. c) dP/dt = kt with P(0)=P0 and k>0. d) dP/dt = kt with P(0)=P0 and k<0. e) dP/dt = kP with P(0)=P0 and k>0. f) dP/dt = kP with P(0)=P0 and k<0. g) dP/dt = kP(1-P/M) with P(0)=P0 and M, k>0

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A scientist is studying three different cultures of bacteria {labeled "A", "B" and "C"} and wants to mathematically model the bacterial change of each type. To do this, the scientist decides to collect data for 25 consecutive days and builds the following scatter diagrams where the horizontal axis corresponds to "t" and the vertical axis to the amount of bacteria present in the culture P = P (t)

Help the scientist decide which mathematical model (initial value problem) to use for each of the three types of crops. To do this, associate each of the graphs above with one of the following initial value problems.

Crop type A

a) dP/dt = k with P(0)=P0 and k>0.
b) dP/dt = k with P(0)=P0 and k<0.
c) dP/dt = kt with P(0)=P0 and k>0.
d) dP/dt = kt with P(0)=P0 and k<0.
e) dP/dt = kP with P(0)=P0 and k>0.
f) dP/dt = kP with P(0)=P0 and k<0.
g) dP/dt = kP(1-P/M) with P(0)=P0 and M, k>0.
h) dP/dt = kP(1-P/M) with P(0)=P0 and M, k<0.

Crop type B

a) dP/dt = k with P(0)=P0 and k>0.
b) dP/dt = k with P(0)=P0 and k<0.
c) dP/dt = kt with P(0)=P0 and k>0.
d) dP/dt = kt with P(0)=P0 and k<0.
e) dP/dt = kP with P(0)=P0 and k>0.
f) dP/dt = kP with P(0)=P0 and k<0.
g) dP/dt = kP(1-P/M) with P(0)=P0 and M, k>0.

Crop type C

a) dP/dt = k with P(0)=P0 and k>0.
b) dP/dt = k with P(0)=P0 and k<0.
c) dP/dt = kt with P(0)=P0 and k>0.
d) dP/dt = kt with P(0)=P0 and k<0.
e) dP/dt = kP with P(0)=P0 and k>0.
f) dP/dt = kP with P(0)=P0 and k<0.
g) dP/dt = kP(1-P/M) with P(0)=P0 and M, k>0.

Cultivo Tipo "A"
1200000
1000000
800000
600000
400000
Cultivo Tipo "C"
200000
3000
2500
0 O 0 O O O
10
15
20
25
2000
Tiempo (t)
1500
1000
Cultivo Tipo "B"
1200
500
1000
10
15
20
25
800
Tiempo (t)
600
400
200
Activar Windows
Ve a Configuraora
10
15
20
25
Tiempo (t)
Cantidad de Bacterias (P)
Cantidad de Bacterias (P)
Cantidad de Bacterias (P)
Transcribed Image Text:Cultivo Tipo "A" 1200000 1000000 800000 600000 400000 Cultivo Tipo "C" 200000 3000 2500 0 O 0 O O O 10 15 20 25 2000 Tiempo (t) 1500 1000 Cultivo Tipo "B" 1200 500 1000 10 15 20 25 800 Tiempo (t) 600 400 200 Activar Windows Ve a Configuraora 10 15 20 25 Tiempo (t) Cantidad de Bacterias (P) Cantidad de Bacterias (P) Cantidad de Bacterias (P)
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