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3 years ago

Please someone help me answer this ASAP

Mathematics

1 answer:

Vsevolod [243]3 years ago

5 0

Answer:

0.28 represents the growth factor

Step-by-step explanation:

Given

$f(x) = 5719(0.28)^x$

Required

What does 0.28 represents

In a function:

$y = ab^x$

b represents the growth factor.

By comparison:

$b = 0.28$

So, this implies that: 0.28 represents the growth factor

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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:

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

(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

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

8 0

4 years ago

24 tenths greater then or less then or equal to 2.5

Dmitry_Shevchenko [17]

24 tenths is 2.4 so it is less than 2.5

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4 years ago

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3 years ago

If you flip a coin 92 times, what is the best prediction possible for the number of times it will land on tails?

slamgirl [31]

Answer:

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Step-by-step explanation:

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