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

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.