Extreme heat applied to a colony of microorganisms causes the size P of the colony, measured in grams, to decrease according to the exponential decay model dP/dt=−0.4P, where the time t is measured in hours. The size Q of a second colony of microorganisms, also measured in grams, decreases at the constant rate of 1 gram per hour according to the linear model dQ/dt=−1. If at time t=0 the first colony has size P(0)=2 and the second colony has size Q(0)=3, at what time will both colonies have the same size?

The populations both colony have the same size after 2.156 hours.

Given that,

The size P of the colony, measured in grams, to decrease,

According to the exponential decay model dP/dt=−0.4P,

Where the time t is measured in hours.

The size Q of a second colony of microorganisms, also measured in grams, decreases at the constant rate of 1 gram per hour

According to the linear model dQ/dt=−1.

If at time t=0 the first colony has size P(0)=2 and the second colony has size Q(0)=3,

We have to determine,

What time will both colonies have the same size.

According to the question,

Separate the variables and integrate,

Using initial condition to find C.

Substitute c = 2 in the equation,

Again, integrate the second function,

Use initial condition to find C.

Then ,

On comparing both the equation to get the value of t,

Hence, The populations both colony have the same size after 2.156 hours.

To know more about Integration click the link given below.

link

Step-by-step explanation:

dP/dt = -0.4P

Separate the variables and integrate.

dP/P = -0.4 dt

ln|P| = -0.4t + C

P = Ce^(-0.4t)

Use initial condition to find C.

2 = C^(0)

C = 2

P = 2e^(-0.4t)

dQ/dt = -1

Integrate.

Q = -t + C

Use initial condition to find C.

3 = 0 + C

C = 3

Q = -t + 3

Set the two equal.

2e(-0.4t) = -t + 3

Use a calculator to find t.

t = 2.156

The populations have the same size after 2.156 hours.

stew reads at the fastest rate of 265 words per minute.

step-by-step explanation:

it's a given that felicia reads at 260 word per minute and on connie's graph we can see that she reads 200 words per minute. since stew's table tells us that he read 795 in 3 minutes, we can divide 795 by 3 to find out how many words he reads per minute.

795/3 = 265

stew reads 265 words per minute - he reads at the fastest rate since felecia reads at 260 words per minute and connie reads at 200 words per minute.

stew (265) > felecia (260) > connie (200)

homozygous. one is homozygous, while two is heterozygous.