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8_murik_8 [283]
3 years ago
5

Rabbits in a colony breed and give birth to baby rabbits. What model best describes the total number of rabbits in the colony ov

er time?
A) Exponential Function

B) Quadratic Function

C) Linear Function
Mathematics
1 answer:
zimovet [89]3 years ago
8 0

Answer: A) Exponential Function

Step-by-step explanation:

Hi, an exponential function describes best the total number of rabbits in the colony over time, because the population tends to multiply by a specific rate over time.

An exponential function can be described as a growth function, for example in the form:

A = P (1 + r) t  

Where:  

p = original population  

r = growing rate (decimal form)  

t= years  

A = population after t years  

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Step-by-step explanation:

\bf➤ \underline{Given-} \\

\sf{x^{2013} + \frac{1}{x^{2013}} = 2}\\

\bf➤ \underline{To\: find-} \\

\sf {the\: value \: of \: x^{2022} + \frac{1}{x^{2022}}= ?}\\

\bf ➤\underline{Solution-} \\

<u>Let us assume that:</u>

\rm: \longmapsto u =  {x}^{2013}

<u>Therefore, the equation becomes:</u>

\rm: \longmapsto u +  \dfrac{1}{u}  = 2

\rm: \longmapsto \dfrac{  {u}^{2} + 1}{u}  = 2

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<u>Now substitute the value of u. We get:</u>

\rm: \longmapsto {x}^{2013}  = 1

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<u>Therefore:</u>

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★ <u>Which is our required answer.</u>

\textsf{\large{\underline{More To Know}:}}

(a + b)² = a² + 2ab + b²

(a - b)² = a² - 2ab + b²

a² - b² = (a + b)(a - b)

(a + b)³ = a³ + 3ab(a + b) + b³

(a - b)³ = a³ - 3ab(a - b) - b³

a³ + b³ = (a + b)(a² - ab + b²)

a³ - b³ = (a - b)(a² + ab + b²)

(x + a)(x + b) = x² + (a + b)x + ab

(x + a)(x - b) = x² + (a - b)x - ab

(x - a)(x + b) = x² - (a - b)x - ab

(x - a)(x - b) = x² - (a + b)x + ab

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