In 1994, the moose population in a park was measured to be 3080. By 1997, the population was measured again to be 3320. Of the population continues to change linearly: Find a formula for the moose population, P , in terms of t , the years since 1990

the formula for the moose population is P(t) = 80t + 2760

Step-by-step explanation:

To get the the formula of the population which changes linearly we start by;

let x be the number of years since year 1990 and y be the number of population measured.

in year  1994 x = 4, y = 3080

            1997 x = 7, y = 3320

we have just gotten two points on a graph which are (4, 3080) and (7, 3320).

Using the slope formula  m =

by substituting both points into the equation

m = (3080 - 3320) / (4 - 7)

m = (-240) / (-3)

m =  80

After getting the slope, we will use the point slope formula to get the equation of the line.  (NOTE: Also either points will arrive at the same result)

point-slope formula =

by substituting the first point into the equation and the slope,

             y - 3080 = 80 (x - 4)

             y - 3080 = 80x - 320

by adding 3080 to both sides

             y - 3080 + 3080 = 80x -320 + 3080

            y = 80x + 2760

so by replacing the formula in terms of P and t, we replace y with P(t) and x with t

          P(t) = 80t + 2760

also by using the second point into the equation and the slope,

             y - 3320 = 80 (x - 7)

             y - 3320 = 80x - 560

by adding 3320 to both sides

           y - 3320 + 3320 = 80x - 560 + 3320

            y = 80x + 2760

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

3x + 18 = 147°

step-by-step explanation:

3x + 18 = 147°, because the value of the central angle is equal to the value of the arc formed by it.

i hope i you.