Write an equation that models the bee population (b), (w) weeks after it is first measured. You'll use the variable b for the bee population and the variable w for the weeks after it is first measured.

The required equation that models the bee population (b) is y = 2000x + 500

The equation of a line in slope-intercept form is expressed as y = mx + b

where;

Using the coordinate points on the graph (2, 2000) and (3, 4000)

Get the slope of the line

Since one of the coordinate points lies on the y-axis at (0, 500), hence the y-intercept is 500.

The required equation that models the bee population (b) is y = 2000x + 500

Learn more on equation of a line here: link

b = 2000w + 500

Step-by-step explanation:

Here, we want to write a linear equation

The general form is ;

y = mx + c

where m is the slope and c is the y-intercept

the value of c is 500

To get the slope, we use any two points on the line and apply the slope formula

This will be;

(2,2000) and (3,4000)

m = (y2-y1)/(x2-x1)

m = (4000-2000)/3-2 = 2000/1 = 2000

So the equation is;

b = 2000w + 500

the correct functions are

h(x) = 3x + 2  

g(x) = 2^x

step-by-step explanation:

i proceed to calculate the different values ​​of k (x)

case 1)  k(x) = g(x) ∘ h(x)

g(x) ∘ h(x)=g(h(x))

k(x) = [2]^[3x + > is the option  4. k(x) = 2^(3x + 2 )

case 2)  k(x) = g(x) + h(x)

k(x) = [2^x]+[3x + 2]=2^x+3x+> is the option  1.) k(x) = 2^x + 3x + 2

case 3)k(x) = h(x) ÷ g(x)

k(x) =  [3x + 2]/[2^x]=3x/(2^x)+2/(2^x)=3x*(2^-x)+2^(1-x)

is the option  3.)   k(x) = (3x)2^(-x) + 2^(-x + 1 )

case 4)k(x) = g(x) - h(x)

k(x) =  [2^x]-[3x + 2]=2^x-3x-> is the option  2.) k(x) = 2^x - 3x - 2 

case 5)  k(x) = g(x) × h(x)

k(x) = [2^x]*[3x + > is the option  5.) k(x) = 2^x(3x + 2)

case 6)k(x) = h(x) ∘ g(x)

h(x) ∘ g(x)=h(g(x))

k(x)=3*[2^x]+> is the option  6. k(x) = 3(2^x) +2