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3 years ago

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What does the expression 1.5a + 2b represent

1 answer:

madreJ [45]3 years ago

8 0

Represents me getting points

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Let P(t) be a population at time t. A simple population model supposes the rate of growth of the population is proportional to t

jeka94

Answer:

$(a) \dfrac{dP}{dt} =k P(t)\\(b)P(t)=Ce^{kt}$

(c) $P(10)\approx 272$

(ii) $P(1000)\approx 26.88 \times 10^{44}\\$

Step-by-step explanation:

(a)The rate of growth of the population is proportional to the population, this is written as:

$\dfrac{dP}{dt} \propto P(t)\\$Introducing our proportionality constant, k\\ \dfrac{dP}{dt} =k P(t)$

(b)

$\dfrac{dP(t)}{P(t)} =k dt\\$Take the integral of both sides\\\int \dfrac{dP(t)}{P(t)} =\int k dt\\\ln P(t)=kt+C, $C a constant of integration\\Take the exponential of both sides\\e^{\ln P(t)}=e^{kt+C}\\P(t)=e^{kt}\cdot e^C $, (Since e^C$ is a constant, we then have:)\\P(t)=Ce^{kt}$

(c)

Suppose the net birthrate of the population is .1, and the initial population is 100.

k=0.1

P(0)=100

Substitution into P(t) gives:

$100=Ce^{kX0}$

C=100

Therefore:

$P(t)=100e^{0.1t}$

(i)When t=10

$P(10)=100e^{0.1 \times 10}\\=271.8\\\approx 272$

(ii)When t=1000

$P(1000)=100e^{0.1 \times 1000}\\=26.88 \times 10^{44}\\$

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4 years ago

Throughout Lewis Carroll's book, Alice's Adventures in Wonderland, Alice's size changes. Her normal height is about 50 inches ta

alexandr402 [8]

Answer:

The answer is 75 inches.

Step-by-step explanation:

If Alice is 10 inches, she is 2/3 as tall as the door. At her regular height, to be 2/3 as tall as the door the door would have to be 75 inches high.

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3 years ago

Arrange the given polynomial in descending order.<br> 3x+7x +1

Mashutka [201]

Answer:

10x + 1

Step-by-step explanation:

First, combine any like terms. Then make sure to rewrite in descending order.

3x + 7x + 1 <== combine any like terms

10x + 1 <== arrange in descending order

Hope this helps!

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3 years ago

Write a function rule for “The output is 5 less than the input.” Let x be the input and let y be the output.

Arisa [49]

The output is 5 less than the input is equivalent to the
input is five more than the output or x + 5 = y

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3 years ago

What do you think about 11 class maths first chapter 'sets'. today l have an exam.

zavuch27 [327]

Answer:

*CRIES* I DONT UNDERSTAND

Step-by-step explanation:

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3 years ago