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3 years ago

Please help!

1 answer:

8 0

<span>(x – h)^2 + (y – k)^2 = r<span>^2

this equation is a derivative of the equation of a circle

x^2 + y^2 = r^2
This is from the origin. If we move the in x or y then the radius will change positions in x or y

with h = -3 and k = 1

we can plug in each set of numbers and solve.

we find Z to be on the circle edge!</span></span>

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the world population was 2560 million in 1950 and 6,080 million in 2000. assume the growth rate of the population P'(t) is propo

tatyana61 [14]

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The population's growth rate is modeled by the differential equation

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This equation is separable, and we can solve easily:

$\dfrac{\mathrm dP(t)}{\mathrm dt}=kP(t)\iff\dfrac{\mathrm dP(t)}{P(t)}=k\,\mathrm dt$
$\implies\displaystyle\int\frac{\mathrm dP}P=k\int\mathrm dt$
$\implies \ln|P(t)|=kt+C$
$\implies P(t)=e^{kt+C}=e^{kt}e^C=Ce^{kt}$

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$2560=Ce^{0k}=C$

and $P(50)=6080$ , which means

$6080=2560e^{50k}\implies \dfrac{19}8=e^{50k}$
$\implies 50k=\ln\dfrac{19}8$
$\implies k=\dfrac1{50}\ln\dfrac{19}8\approx0.0173$

So the population is modeled by

$P(t)=2560e^{0.0173t}$

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3 years ago