The population of rabbits on an island is growing exponentially. In the year 1994, the population of rabbits was 9600, and by 2000 the population had grown to 18400. Predict the population of rabbits in the year 2009, to the nearest whole number.

49243

Step-by-step explanation:

Given that the population of rabbits on an island is growing exponentially.

Let the population,

where, and b are constants, t=(Current year -1994) is the time in years from 1994.

In 1994, t=0, the population of rabbit, P=9600, so

So,

and in 2000, t=2000-1994=6 years and population of the rabbit, P=18400

b=0.109

On putting the value of P_0 and b, the population of the rabbit after t years from 1994 is

In 2009, t= 2009-1994=15 years,

So, the population of the rabbit in 2009

Hence, the population of the rabbit in 2009 is 49243.

stethere all not eveanp-by-step explanation:

a.   we have two

lines:   y = 4-x   and  

y = 8-x^-1

given two simultaneous equations that are both to be

true, then the solution is the points where the lines cross. the intersection is

where the two equations are equal. therefore the solution that works for both

equations is when

4-x = 8-x^-1

this is where the two lines will cross and that is the

common point that satisfies both equations.

b.   4-x = 8-x^-1

  x           4-x       8-x^-1

-3           7        

8.33

-2           6         8.5

-1           5         9

  0           4        

-

  1           3        

7

  2           2        

7.5

  3           1         7.67

the table shows that none of the x values from -3 to 3 is

the solution because in no case does

4-x = 8-x^-1

to find the solution we need to rearrange the equation to

find for x:

4-x = 8-x^-1

multiply both sides with x:

4x-x^2 = 8x-1

x^2+4x-1=0

x= -4.236, 0.236

therefore there are two points that satisfies the

equation.

find y:  

x=-4.236

y = 4-x   = 4 – (-4.236)

= 8.236

y = 8-x^-1 =   .236)^-1

= 8.236

x=0.236

  y = 4-x   = 4 – (0.236) = 3.764

y = 8-x^-1 =   8-(0.236)^-1

= 3.764

thus the two lines cross at 2 points:

(-4.236, 8.236) & (0.236, 3.764)

c.   to solve

graphically the equation 4-x = 8-x^-1

we would graph both lines: y = 4-x   and   y

= 8-x^-1

the point on the graph where the lines cross is the

solution to the system of equations.

just graph the points on part b on a cartesian coordinate

system and extend the two lines.   the

solution is, as stated, the point where the two lines cross on the graph.

step-by-step explanation:

mark brainliest!