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.

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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.

y=mx+

answer: there are x+184 pages in olivia's book.

step-by-step explanation:

let the total number of pages in the book which olive has already read be x.

then if olive has 184 pages left to read, then the total number of pages are in olive's book= pages she has read+pages she has left to read

therefore, the total number of pages in olivia's book=

hence, there are x+184 pages in olivia's book.