Find the value of X.

The population of rabbits on an island is growing exponentially. In the year 1990, the population of rabbits was 1200, and by 19

kobusy [5.1K]

Answer:

2023 rabbits

Step-by-step explanation:

The exponential model consists of the following expression:

$y = A \cdot r^{t}$

Where:

$A$ - Initial population.

$r$ - Increase rate.

$t$ - Time

$y$ - Current population.

The initial population and increase rate are, respectively:

$1200 = A \cdot r^{0}$

$A = 1200$

$1700 = 1200 \cdot r^{4}$

$r^{4} = \frac{1700}{1200}$

$r^{4} = \frac{17}{12}$

$r = \sqrt[4]{\frac{17}{12} }$

$r \approx 1.091$

The exponential model that predicts the population of rabbits is:

$y = 1200\cdot 1.091^{t}$

Lastly, the expected population for the year 1996 is:

$y = 1200\cdot 1.091^{6}$

$y\approx 2023.624\,rabbits$

5 0

3 years ago

What is the volume of the composite figure? 1,200 units3 4,400 units3 5,040 units3 6,000 units3

swat32

Answer:

6000

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

Sin theta+costheta/sintheta -costheta+sintheta-costheta/sintheta+costheta=2sec2/tan2 theta -1

sleet_krkn [62]

$\dfrac{sin\theta + cos\theta}{sin\theta-cos\theta}+\dfrac{sin\theta-cos\theta}{sin\theta+cos\theta}=\dfrac{2sec^2\theta}{tan^2\theta-1}$

From Left side:

$\dfrac{sin\theta + cos\theta}{sin\theta-cos\theta}\bigg(\dfrac{sin\theta+cos\theta}{sin\theta+cos\theta}\bigg)+\dfrac{sin\theta-cos\theta}{sin\theta+cos\theta}\bigg(\dfrac{sin\theta-cos\theta}{sin\theta-cos\theta}\bigg)$

$\dfrac{sin^2\theta+2cos\thetasin\theta+cos^2\theta}{sin^2\theta-cos^2\theta}+\dfrac{sin^2\theta-2cos\thetasin\theta+cos^2\theta}{sin^2\theta-cos^2\theta}$

NOTE: sin²θ + cos²θ = 1

$\dfrac{1 + 2cos\theta sin\theta}{sin^2\theta-cos^2\theta}+\dfrac{1-2cos\theta sin\theta}{sin^2\theta-cos^2\theta}$

$\dfrac{1 + 2cos\theta sin\theta+1-2cos\theta sin\theta}{sin^2\theta-cos^2\theta}$

$\dfrac{2}{sin^2\theta-cos^2\theta}$

$\dfrac{2}{\bigg(sin^2\theta-cos^2\theta\bigg)\bigg(\dfrac{cos^2\theta}{cos^2\theta}\bigg)}$

$\dfrac{2sec^2\theta}{\dfrac{sin^2\theta}{cos^2\theta}-\dfrac{cos^2\theta}{cos^2\theta}}$

$\dfrac{2sec^2\theta}{tan^2\theta-1}$

Left side = Right side <em>so proof is complete</em>

8 0

3 years ago

Read 2 more answers

Please help me with the questions

Grace [21]

Answer:

x = 5

x = 2

Step-by-step explanation:

2(2x + 4) = 8x - 12

2x + 4 = 4x - 6

x + 2 = 2x - 3

x = 5

Question 17

8/4 = (x + 2)/(2x - 2)

2(2x - 2) = x + 2

4x - 4 = x + 2

3x = 6

x = 2

4 0

2 years ago

a pastry recipe calls for 3 cups of flour to make 8 serving .how many cups of flour are needed to make 6 serving

ser-zykov [4K]

If you would like to know how many cups of flour are needed to make 6 servings, you can calculate this using the following steps:

3 cups of flour ... 8 servings
x cups of flour = ? ... 6 servings

3 * 6 = 8 * x
18 = 8 * x /8
x = 18/8
x = 9/4
x = 2 1/4 cups of flour

The correct result would be 2 1/4 cups of flour.

5 0

3 years ago