Question

The population of Bunny Kingdom is monitored by a bunny enthusiast, who notices that the population of bunnies doubles every three years. If the initial population was 200 bunnies, how many years would it take for the population of bunnies to hit 12800?

Answer 1

Answer:

64 years

Step-by-step explanation:

Divide 12800 by 200.

Answer 2

Answer:

Number of years it would take for the population of bunnies to hit 12800 is 18 years.

Step-by-step explanation:

Given, In the Bunny Kingdom the population of bunnies doubles every three years.

Initial population of bunnies = 200

This is the problem of Growth modeling.

• For this type of problem, we should derive an equation that describes the growth pattern.
• The population growth or decay is usually modeled with exponential equation.

Let 'y' be the final population of bunnies.

Let the equation for population growth is y = $ax^{t}$

where t is in years.

To determine the values of a,x, we use the conditions given.

At t = 0, y = 200  ......(1)

At t = 3, y = 400  .......(2)

Using Condition (1)

200 = a*$x^{0}$

a = 200

Using Condition (2)

400 = 200*$x^{3}$

$x^{3}$  = 2

x = $2^{\frac{1}{3} }$

Therefore, the equation for bunny population growth is $y = 200(2)^{\frac{t}{3} }$

To calculate the value of 't' for which y = 12800.

12800 = 200*$2^{\frac{t}{3} }$

64 = $2^{\frac{t}{3} }$

$2^{6}$ = $2^{\frac{t}{3} }$

Since the base of L.H.S, R.H.S are equal, we can equate the powers.

6 = t/3

t = 18

Number of years it would take for the population of bunnies to hit 12800 is 18 years.

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